If you Google this word you'll get so many hits your brain will implode. Let's take it one step at a time.
Curry is an English word which is used to refer to vegetable and/or meat dishes that are stew-like, that is to say small pieces in a gravy, with Asian spices. This is generally served with rice and/or a flatbread. Because there are a lot of these type of dishes in India, it has often been mis-used to refer to most or all Indian food which is quite wrong. The word curry really refers to the gravy arrangement.
However it's not as wrong as what happened next. The vague idea of an Indian flavour gave rise to the idea of "curried", in other words, foods cooked with Indian flavours. As there are hundreds of different spices used in India, and two dishes can be cooked with exclusively different ones and still be seen from the West as curry, this is pretty hard to explain, but people seem to know what they mean.
Possibly the greatest silliness is the idea of a "curry sauce", which could be seen to be a "gravy gravy". But there it is, people say it all the time, AND, again....everyone knows what they mean.
I have joked over the years that the typical British way of serving Chili con Carne over rice, makes the dish a Mexican curry, but I get funny looks. Prove me wrong.
Now then, you can become an Indian food purist. A real snob. Go ahead.
OR, you can say, "well, I'm not Indian, but I like this type of food, can I just make it up as I go along?".
What do you think Indian cooks do?
Look - I'm English. Curry is the national dish of England. The first curry house opened in England in about 1780, and we never looked back. Some of the top dishes in the world thought of as Indian were in fact created in England. I grew up on the stuff, I am intimate with it. What I cook is NOT Indian food. So don't bother telling me it isn't, I know. I cook English curry, and I do it well.
Here is the non-Indian way of making avant garde curry, as a quick, tasty, and cheap meal. I do it all the time.
First choose your base. Meat or vegetable? This is a great dish for vegetarians (or people trying to save money by skipping meat) because the rich flavour replaces the umami missing from non-meat meals. Chick peas, lentils, and beans are typical ingredients in a curry anyway, and used instead of meat they make it hearty.
If you are using meat, decide if it needs long slow cooking or not. Chicken breast does not. Lamb or beef, the cuts intended for stew anyway, need to be started at least 1 1/2 hours before you plan on eating. Dried legumes need about the same time. So if it's to be a long cooking time, plan ahead accordingly (you can also use a slow cooker).
If it's all vegetable, it doesn't take quite so long, although some root vegetables benefit from longer cooking.
Start by heating some oil or the traditional Indian ghee (clarified butter, tastes like heaven) and sauté some onions in it. You add your spices NOW, but we'll discuss that in a minute. The hot fat draws the flavours out. Add diced meat, brown it, and any veggies that you need to add now (if unsure, ask me). I would certainly add carrots, rutabaga, and potatoes at this point. Also add garlic now, and lots of it.
Once the meat is brown, and the veggies are tender, you need to add liquid. It doesn't really matter what it is, it can be a frugal stock (when flat broke I've used water, frankly), but you can't go wrong with passata (tomato juice) and/or coconut milk. I often use half and half. If you don't like the taste of coconut, fear not. You won't taste it. But it lends a creaminess without that risk of burning you'd get from milk. Cover everything with your liquid. Now is when you add legumes. Put a lid on this and simmer it until everything is tender, adding short-cook vegetables as appropriate. Test the flavour 10 minutes before serving, as you can add a bit more spice if need be then.
What are good vegetables to use? This is where English curry differs from Indian curry. Use what you have and what you like. In India - a HOT country - lots of exotic vegetables grow. Do you need them? No. Indian cooks use them because that's what they have. I use carrots, peas, potatoes, cauliflower, zucchini...whatever is lying around.
Now then, if you want to use chicken breast, or fish, or sausage (oh yes you can), it doesn't need so long. You can even do a stir-fry version. Just figure out how long each ingredient takes to cook, plan ahead.
You can use leftovers, and this is a perfect way to hide things that didn't turn out well. No, I'm quite serious, If you have a stew, a soup, or anything that went wrong, you can recycle it into curry. I hate waste.
You can tip everything raw into a slow cooker in the morning and come home in the evening to a fantastic curry. It won't be as good, but it'll be good enough. Meat is always better if it is browned first, don't ask me why (I'll tell you in the Fall, I'm taking a gastronomy course!) it just is. But it will be OK effectively boiled with spices.
So, the spices.
You can cheat. You can buy "curry powder". Each brand is different and you can find a favourite, or just vary it up a bit. OR, you can use this ratio:
3 parts coriander
3 parts cumin
1 part turmeric
1 part ginger
1 part cayenne
a little cardamom (optional)
Mix this in whatever amounts you like, and then use 4-6 tablespoons of this. If you are a bit nervous, use less at the start, and adjust at the end. You can reduce the cayenne (or save it until the end) if you prefer a mild curry, as this is the heat. There are lots of other spices that can be used, but you will get a flavourful sauce with this. I should mention, at this point that a lot of people are using cinnamon in curries, and you can too if you want, but I don't.
You will also need some salt and pepper, about a teaspoon of each is plenty.
So, when everything is tender, and you are happy with the spices, serve with boiled rice and/or naan bread.