So I just returned from 14 days in Madrid. It was my first time in Spain - I loved it, had a great time, had some great food. That said, I have some tips for first timers, based on my experiences. Take them for what you want, I'll try to keep them brief. This is NOT a restaurant recommendation/review post.
I wasn't going to post based on my experiences because I didn't have any specific advice I felt the need to relay - but something happened several times while I was there that I've never seen before in all my european travels. 5 times I was in a restaurant (different restaurants) - had an American family enter the restaurant, ask if they spoke english or had english menu's - none did - they sat down and after 5 minutes they got up and left. I felt so bad for them and experienced some of their frustrations at times - so wanted to just put these out there . . .
1) Don't expect a lot of english to be spoken, understood, or translated menus.
Of course this is a generalization but if you expect anything other than this you'll be frustrated. I am not one to expect a foreign country to speak English but there was significantly less heard/translated than in any other European country I've visited. That said, the people were very nice and happy to try to help with what they could. In fact, a few times I just took to saying "I'd like to eat but I don't understand. Help me." (Granted i studied Spanish for 6 years in High-School - which was a LONG time ago but I speak some Spanish).
2) DOWNLOAD THE NEW GOOGLE TRANSLATE APP
I rarely if ever recommend an app. But the new Google Translate has a feature that is game changing. They recently bought "World Lens" and integrated it into their app for free. It uses the phone's camera to instantly translated printed text. You don't take a picture, you read whatever is on the screen in English rather than in Spanish (for example). It requires no internet/cell network connection. It is AMAZING and I used it on menus almost every time! It is game changing for foreign travel.
3) You will have to put on your "big boy travel pants" if you want to eat in casual places - the good ones are always crowded, the bad ones are always empty.
I understand why so many tourists eat in the "Museo de Jamon" (and the like) in Madrid. The menu has pictures and you can just point. But if you want to eat in local, small restaurants/bars, you're going to have to be a little brave. The Spanish are loud and friendly - but it is intimidating and leads to the impression that everyone knows each other and you're the odd one out. The quarters are tight. The front door is going to be 1/2 blocked by smokers. There is no rhyme or reason to eating at the counter in a taverna. Just find an open spot and go for it. When you're not fluent in Spanish it is intimidating. But go for it.
I'd tell my friends to start at the Mercado San Miguel to get used to the whole thing. Touristy but crowded, you'll have to squirm for space, you can order from several places at once and share a communal table in the middle .. . .
4) For foodies who've made it this far - go to the Mercados but also go to a Corte Igles.
I loved the Mercados - I went to almost all of them in central Madrid. But honestly I was most blown away by my experience at the supermercado in the basement of the Corte Igles (in Salamanca on Ortega y Gasset and Velazquez I think was the corner (could have been Serrano) - though I'm told most have them). If you've never done a supermarket like these, they are in the basement of essentially a department store (think Macy's), so no you're not really in the wrong place. I suggest going for the charcuterie area alone. I've never seen the volume of charcuterie - not to mention whole leg jamon - as I saw in Spain - and in the basement of Corte Igles. And this was in the basement of a "Macy's" essentially. I went several times and was just . . . jealous.
I hope you go, I hope you have fun!
Oh, one last thing - I never really got used to how the Spanish eat (again, my first visit - only to Madrid - and mainly small tapas places). They ate relatively few green vegetables (thought the markets were full of them) - and lots of pork. Lunch at 3pm and dinner at 10pm never felt how my body wanted to eat. And as a tourist, i could never figure out when things were going to be open and when they were going to be closed (tourist attractions, markets, restaurants, etc). I did a lot of research before I went and the reality versus what was posted never quite lined up.
I only posted these to just help you get in a good head space before you go - so you can roll with things and enjoy. I talked with 3 other American's who had all recently moved to Madrid and they all said "I'm so glad you said that" because they had similar experiences as I did.