To open a bank account in Madrid you may need your foreigner’s identity number or numero de identidad de extranjer@ (NIE). This will either be included in the temporary visa in your passport or you will have to wait to get your visa card (tarjeta de identidad de extranjer@ or TIE) to get the number. Some bank branches will need you to have the number and card to open the account whereas others will be fine with you using your passport number, and coming in later once you finally have your identity card. To open an account you will almost definitely need to use Spanish, and remember you can generally bring a friend with you to help.
I opened an account with BBVA, using my NIE which was included in my temporary passport visa, and just had to come in (to the same branch) once I had my physical foreigners card too. The branch you use to open the account will be considered your main branch, and you will need to return to the same one to take care of logistics. I chose a branch out in one of the little pueblos that I worked at, which had the advantage of almost never having a line of people waiting, but the disadvantage of being far away and the fact that I only went to that town twice a week.
I have heard great things about the bank EVO. They are small and don’t have many branches, but you can take out money from any bank’s ATM (cajero) without having to pay a fee.
Madrid’s public transportation system is absolutely fabulous. I highly recommend choosing the area you live in based on the metro stops surrounding it, and the difference it makes if you have a long commute (as people in the Auxiliares program usually do). I chose to live in Malasaña and although this wasn’t the ideal location for the shortest commute (I could have lived closer to Moncloa, the bus station that connected me to my bus to my pueblo) living in Malasaña did set me up in the center of town, right next to Tribunal (line 1) and close enough to line 3 that although it took me 20 minutes to reach Moncloa, it also only took me 20 minutes to get south to La Latina or Lavapiés.
If you will be taking the metro a lot, it is recommended that you purchase an abono transporte, which is essentially a metro pass that you put money on every month, the amount of money depending on how far out of the city you have to commute. The center is zone A1, then there is zone A2, A3, B1, B2, and so on. I ended up having to go out to zone C1 everyday, making my monthly payment a heart wrenching 86€! If you are under the tender age of 23, you get a youth discount, but alas, I was not so fortunate.
I got a Spanish SIM card though a company called Orange, and got a plan called La Ballena (the whale) which got me some internet and some phone calls/SMS. I hear Yoigo is a pretty good company as well.
Whatever you do, don’t use Vodafone. In addition to my own bad experience with the company, I have heard an endless amount of horror stories about them I will not waste your time with.
Some phone companies will want to have your foreigner’s card number (NIE, or numero de identidad de extranjer@) which you may have gotten on your temporary visa in your passport, but you also may have to wait to acquire. It’s fairly random who has theirs stamped in their passport or not. Luckily if you don’t have your NIE, some of the company branches won’t care, and will let you use your passport number. It’s a toss up to figure out who will and won’t, and you will soon learn that this sort of attitude is fairly common in Spain, and that the same thing will happen if you attempt to open a bank account (this is a prime example of when the Auxiliar page on Facebook comes in handy for questions on specific phone and bank branches).