Do you speak any Spanish? Spain does not have the best reputation for having ubiquitous English speakers but I didn't have many problems in Madrid. I actually found a lot of English speakers when I was there, mostly younger folk though, and didn't have many problems with my poor Spanish. I pretty much got by just saying "claro" or "vale" a lot.
You should know basic stuff about food, like that some bars/restaurants will close during siesta, and at lunch you'll want to look for the menú del día (basically a fixed price meal with two courses, drink and sometimes dessert). Carta is Spanish for menu, don't get them confused. If you want beer order a caña, this is basically a small glass about a half pint. Don't get paella in Madrid, it's not authentic and is just used to bait unsuspecting tourists.
One thing about Spain (and Madrid especially) that nobody told me before I went - there are tons of great pastelerías and bakeries in Madrid. And I'm not talking about churros, I'm talking about napolitanas and other pastries. If you have a sweet tooth, you will be in heaven.
Madrid is a lot like NYC, lot of people, lot of tourists, very crowded in the major pedestrian areas. A lot of very beautiful, pleasant neighborhoods though once you get outside of the center. One thing I will note, and this happened everywhere in Spain, I am a blond haired man and I got stared at a lot by people when I was walking around. I guess blond hair is not that common in Spain.
If you like art you should definitely one of the big 3 museums (Prado, Reina Sofia, Thyssen). They get very busy even in the "off season" so you should look into getting tickets as soon as possible. I've listed in these order of size and amount of time they are likely to take. Prado is basically the house of Velazquez and Goya, so if you're really interested in the height of Spanish art, visit that. Reina Sofia and Thyssen are better for a modern art lover, but Thyssen will be much less crowded than the other two. There's a pass available that gets you entrance to all three and it's good for like a year or something, so if you don't see them all and are ever able to get back, you can visit the ones you missed.