Summarize:

When you go to an Indian restaurant there are a variety of different dishes that all use the same basic ingredients and technique used in curries. The difference is primarily in thickening agent used:   Korma uses a creamy agent, like coconut milk, yogurt, or cream.  Saag uses greens, usually spinach but sometimes mustard/collard greens.  Madras uses pureed and diced tomato  Vindaloo uses pureed chilies. This technique, used in many restaurants, creates a curry paste of onions, garlic, ginger, and spices, which cooks faster and results in a smoother curry. To make it, use a food processor to grind everything up into a thick paste, then add it to the hot oil after the seeds have crackled. There is no one "curry" recipe out there. Curry is about mixing and matching ingredients using curry cooking technique, as outlined above. Still, to make the most basic, run-of-the-mill curry you would add and cook, in this order:  3 tablespoons vegetable oil or ghee (clarified butter) 1/2teaspoon ground cumin seed 1/2teaspoon ground coriander seed 1 medium onion - finely chopped 4 cloves garlic - peeled and sliced 1.5-inch piece ginger - peeled and thinly sliced 1/2 teaspoon turmeric powder, curry powder, salt 2 mild fleshy green chilies - de-seeded and chopped 5 tablespoons tomato puree or 1 tablespoon (14.8 ml) concentrated tomato paste mixed with 4 tablespoons water You should add spices generously, tasting and sampling every chance you get. Start with a tablespoon of any of following, adding more or less to fit your preferences:  Cumin (essential) Coriander (essential) Turmeric (essential) Ground chili powder Cardamom Cayenne pepper Cinnamon Curry powder Smoked paprika Garam masala Asafoetida (just a pinch, also called "hing")
Understand how different sauces are created. Pulse or blend your ingredients ahead of time for a smoother sauce. Remember that cooking curry is about method, not a specific recipe. Play with the spices you want to add.