You’re in for a treat. Once you start to appreciate Indian food, you’ll never look back. What follows is all off the top of my head, and largely based on the UK and Ireland (though I have eaten Indian a few times in the States) so forgive any inaccuracies.
The Indian sub-continent is so huge that obviously there’s no one single Indian cuisine. I personally love the south-Indian Bel Puri style of delicate potato, coconut and wafer-based cuisine, but they’re specialized and you’re unlikely to find many Bel Puri restaurants around. Also, in many Indian restaurants in India you get a thing called a “Thali”, which is a plate with several indentations, on which several different delicacies are dished up (constantly - every time you finish part, the waiter refills it, until you say “no more!”).
That said, in your ‘standard’ western-style Indian restaurant, there is a kind of a homogenized cuisine which tends to have a lot of stuff that’s derived from Bangladesh and Pakistan. You’ll usually follow the western model of an appetizer followed by an entree. Unless they’re actually in the main dish, vegetables are served as a side-dish, as is rice or bread.
If you’re a novice, then I’d say get some “easy” options before graduating to the more adventurous stuff (what’s “squishy”, then?).
You’re table’s likely to have dips on it. These are usually raita (cooling yogurt and cucumber and/or mint), lime pickle (a very intense flavour - chilli oil-marinated lime), mango chutney (jelly made with mangoes), and chopped onions and tomatoes with mint (can’t remember the name for this). Papadams (or Poppodoms or some other spelling) are a pre-appetizer appetizer, and will probably be brought to your table when you sit down. They’re sort of like a very thin crisp tortilla. Break them on your plate and accompany them with some of the dips.
For an appetizer, I’d recommend tandoori chicken - this is chicken pieces that have been coated in mild spices and yogurt, that’s then cooked in a very hot clay oven (called a tandoor). Served with a tiny salad and some lemon juice to squeeze over. It’s a bit dry, but it’s delicious and you can moisten them with some raita. Onion bhajis are nice - they’re onion fried in dough balls. Pakoras are pastry parcels of meat, potato and vegetables, folded into a triangle and fried (a bit like a chimichanga).
Most Indian entrees are something-in-sauce. The sauce might be very spicy-hot, or very mild, and based on tomatoes, cream/yogurt, or some other thickener more like a gravy. They’ll all have spices in them, but not all have chilli. The standard bases for these dishes might be chicken, lamb (you’re unlikely to find beef, even if the restaurant isn’t run by Hindus, or pork, even if the restaurant isn’t run by Muslims), shrimp, or mixed vegetable.
The safest option of all is the UK’s favourite entree (more popular even than fish and chips now), Chicken Tikka Masala, which isn’t even Indian. This is tandoori chicken (see above) in a mildly flavored sauce of yogurt and spices. It’s lovely. A jalfrezi is a medium-spicy tomato-based sauce. AFAIK rogan josh just means “cooked meat”, and is almost always lamb in spicy gravy. A balti is like a spicy stew with meatballs in it. Ones to avoid: vindaloo (very very hot, though I have to say I really like this, and it’s one of the few dishes that traditionally uses pork), fahl (very very very hot). Anything just called “curry” is usually gravy-based and is quite hot. You can get most of the ingredients in each kind of sauce - e.g. prawn (shrimp) jalfrezi, chicken jalfrezi, vegetable jalfrezi.
Vegetables - most of the exotic names are actually really mundane: aloo means potato, mutter means peas, sag means spinach (palak is very similar, though it’s a different plant), dal means lentils, chana means chick peas (garbanzo beans). Paneer is a form of firm cheese that is often served cubed with vegetables). One very important word that you’ll see everywhere: masala. This just means “mixed”, nothing more. Most veg come in a sauce too, with spices, but are usually very mild. It’s normal to order several vegetable dishes and for everyone to share them.
You then have rice or bread (I wouldn’t have both, myself). Rice is usually of the basmati variety, and is offered in many different forms: boiled, fried, pulau (which just seems to mean with a couple of cardamoms and some food colouring). Nan bread is the most popular - it’s a big soft, doughy flatbread cooked on the inside of the tandoor. You can get this with fruit in it (Peshawari nan), meat (Kashmiri nan), or with garlic and/or coriander. A chapati is a little flatbread like a tortilla. Paratha is a rich flaky fried (I think) bread, made with butter. Traditionally you tear bits off the bread and use it to scoop up the food (right hand only! Never touch anything at the table with your left hand.) or if you’re being very western, tear it and put bits on your plate and eat them with your entree. Again, it’s normal to share the starchy stuff. My philosophy is to keep the starchy stuff as plain as possible, so as not to mask the flavors of the entrees.
That’s all I can think of at the moment. This post has gone on way to long. I’m a bit of an Indian food freak, as you may have guessed.