Whether you want to cook fully vegan or just want to use fewer animal products in your cooking, that's fantastic. Changes in our lives are often great times for growth, so look forward to expanding your palate with some healthy ingredients like tofu, tempeh, nutritional yeast, beans and pulses which you may not cook with much at the moment.
For some people changing a handful of the ingredients they are used to cooking won't be a problem but for others, it might take some adjustment. Remember though most people cycle through a few regular recipes for most of their home-cooked meals. A great place to start is to look at your regular meals and figure out how to veganise them. It won't take you long to figure out vegan versions of most of your staple dishes and you can perfect them over time. Once you have that down pat you can experiment with new recipes that add variety and spice to your roster, and might even come in as new regulars.
Online or in most cities now you can buy vegan alternatives for just about everything, which can be a great place to start, what could be easier than replacing an animal product with something that has been made to look and taste like that animal product. The real health boost, however, is in moving towards a largely whole-foods plant-based diet, but maybe removing animal products is enough to concentrate on at first.
To veganise almost any dish, mainly by looking at the role the animal product played in the dish. Protein, fat, salt, textures, flavour, think about what the particular ingredient is adding to the dish and look for a plant-based analogue.
Protein is a good place to start because it makes you feel full and people are often under the misconception that it is hard to get on a vegan diet.
Pasta is one of my weekly staples, delicious and easy. To make sure it's got plenty of protein I'll generally add french lentils (puuy), canned brown lentils, a can of red kidney beans, or a handful of soy mince to a recipe. Canned beans and lentils are incredibly useful to have in the cupboard to make any meal more substantial. Obviously it is cheaper and more environmentally friendly to cook your own, which a pressure cooker can really help with. You can get dried soy mince (also called TVP) at any health food shop, which I tend to use in moderation, a handful is more than enough in most things. You can also buy frozen soy mince, which is more expensive, including in carbon by needing to be kept cold, but it is generally better if you want to use it in the quantities of regular mince.
Also on the subject of lentils, one of the first crops ever cultivated in Eurasia, there are so many kinds that it is hard to generalise about them. Red lentils cook quickly and go soft, making them great for soups. French and green lentils take a little longer but hold their shape nicely, making them good for pastas. Brown lentils take the longest to cook but are also reputed to be the healthiest and lend themselves well to shepherds pies, and of course curries along with chickpeas. These are the main lentils you'll find in supermarkets, but there is a whole world of them to discover, and they are good sources of iron, protein and many other nutrients.
Pesto is really easy to veganise and full of protein, just blend some basil, salt, garlic, pine nuts and olive oil, or experiment with using blends of other sorts of nuts such as almonds, macadamias and pistachios, and other herbs such as a touch or oregano in with basil, or coriander/cilantro. Usually pesto would have some cheese mixed in so you could put some soy parmesan in but it really isn't needed, and a spoonful of nooch* will do the job anyway.
* Nooch - Nutritional yeast is a secret vegan ingredient. Go to your local health food store, give them the secret vegan handshake and they'll give you some. Try to get one with B12 added to it, and then sprinkle it on everything until you know what you like. Some people get obsessed with it and personally I like it but not "have it on popcorn" like it.
Kidney beans and soy mince lend themselves really well to chillis, as well as refried beans which are great for burritos, tacos etc.
For something like a stir fry, cashew nuts or tofu are a great way to go. I will chop up some tofu and cook it in a little oil, maybe a splash of soy, setting it aside for adding later, there are lots of great pre-marinated tofus, or just put some raw nuts such as cashews in and brown them slightly.
Complete sources of protein are quinoa and soya, so you can put what you want on a bed of quinoa (used much like couscous or rice, and the packets usually have good cooking instructions) and get plenty of protein.
Finally, there are lots of substitutes you can get from health food shops, you can check the website Happy Cow for your closest ones worldwide (as well as nearby restaurants with reviews). Personally, the substitutes I use most regularly are veggie sausages for a quick breakfast fry up, with beans, toast, grilled tomato, and if I'm feeling energetic mushrooms and scrambled tofu.
Veggie burgers are another staple for me, I also usually keep some sort of veggie burger, nut cutlets, bean burgers, wheat protein burgers, in the freezer for quick filling meals on nights when I'm busy (or just feel like a burger which is pretty often). If you have a food processor, it's pretty easy to mix some brown rice, beetroot, brown lentils, and seasonings to make a heap of cheap burgers for putting the freezer and putting between bread, or next to some veggies for a nutritious filling meal.
Dairy replacement is often the hardest one for people because they have a pretty unique texture. The fats in them are probably the main reason we like dairy products, though they also have sugars in the form of lactose, usually salt, and some protein. So replacing fats isn't hard.
In a salad, toast up some nuts, usually cashew nuts, walnuts (in a little soy) or pine nuts, avocado is always good as well. I also like to add tahini to my salad dressing to sneak in some calcium and protein, plus a little miso just because it is awesome and salty.
The cookbook Veganomicon has a recipe for cashew ricotta which is great in lasagnas, for the lasagne topping I'll make a bechamel white sauce to top it, sometimes with a little nutritional yeast added in.
Blended cashews can be made to do just about anything, often with some nooch and lemon juice.
Coconut milk is a great rich alternative to cream, particularly in curries, soups and goes great with lime juice. It has a unique flavour, so I'd only generally use it in something I actually want that flavour for.
In a sandwich or burger, I'll add in some avocado instead of cheese, and this also works really well on a pizza either slightly baked or fresh. Another thing which works really well for pizzas is to make a pesto as a base, giving you plenty of fat and flavour.
Again there are vegan alternatives, the parmesan, yoghurts, soy creams and cream cheeses are all pretty good, experiment with different brands to find your favourite. Alternative cheeses are getting better all the time, with regular new products coming out. The soft cheeses are awesome, but with hard cheeses, I prefer to use them sparingly. Grate it on pizzas, nachos, or into your bechamel, but don't go overboard with it as you might have once done with cow's milk cheese.
As mentioned there's also nutritional yeast which are flakes you can throw in anything, a risotto, a bechamel or your scrambled tofu etc which has a slightly cheesy flavour.
Finally, you can make a tofu-based feta replacement "Tofeta". To make, crumble firm tofu with extra virgin olive oil (a fair amount), salt, dried oregano and crushed garlic. You can use it straight away, or it tastes better if it sits awhile. Use it in sandwiches, on pizzas, in salads, topping on anything really.
A variation is instead of really mashing it into a soft paste (best for sandwiches and pizza), just roughly crumble it into chunks about the size of a kidney bean, then add lots of lemon juice, with all the other stuff mentioned above, and marinate for as long as you can (overnight is best). This makes a greek salad like no other and cheese eaters have said they like it better than real fetta in a greek salad. You can add it to any sort of salad though and it is particularly good in rice salads.
There are just so many plant-based milks to try so it's perhaps the easiest thing to substitute. If you drink takeaway coffee regularly, you can just ask for different ones each time and see how you like them. Keep going through them until you find one you like, even different soys all taste different according to the other ingredients. Personally, I'm an unsweetened oat milk man, but I'm partial to rice milk, soy milk, hemp seed milk, the new coconut milks which don't taste like coconut milk, and almond milk. When I first went vegan I only really liked plant milks added to something, cereal, tea etc, but now my taste buds have changed and I can chug the stuff.
I would advise making sure you get plant-based milk with calcium of around 300mg, which most do these days, but just make sure to check.
Eggs...well you don't really need them in most things. You'll find a million scrambled tofu recipes on the web, and many vegans have their own variation of crumbled tofu, turmeric, soy sauce and onion, often slicing in more vegetables and nutritional yeast, personally, I put oregano and any extra veggies I have lying around in mine.
My favourite cookbook Vegan Planet has a banana pancake recipe I've been cooking variations of regularly for years and everyone loves them, indeed my partner would get me to make them every morning if I would. Last week I use grated apple and blueberries instead of bananas. Another great addition is a handful of quartered strawberries. Anyway, people are always saying "how do you make pancakes without eggs", and I say, "You just do, and it works". Like many things, it's just trying it that is often the hardest part psyschologically.
Vegan cakes and muffins have won cake making competitions against all comers, and in most towns I've lived in there's a cafe or restaurant where you'll be able to try some great vegan cakes. There is also egg replacer which I virtually never use, but if you really need it, it is there and perhaps will give you peace of mind if making a dish which originally asked for an egg.
Finally, I'll give you the tip my friend gave me when I told her I was trying to give an introduction of how to veganise things "take out the animal things, replace with plant things, done!". That's kind of the essence really, you can usually figure out a way to make versions of all your favourite dishes.
You'll spend a little time making the adjustment, but it's not rocket science so experiment and have fun. I guess that's the main thing, take time to enjoy cooking. I love cooking now, and though I wasn't always that way inclined I now treat it as a self-indulgence. If I cook something beautiful for myself I feel I've done something useful and creative in my day. Learning to enjoy the washing up is a little harder though!
Also online there are thousands of blogs, feeds, youtube channels, complete "How to go vegan" course with recipes, facebook groups etc. Like many things it's never been easier and getting into the habit is the important step.
Vegan power and bon appetit to you!