You want to live in a new country, but do you want to be cut-off from the world? No way!
The best way to stay in contact is to nuy a pre-paid "tarjeta" card. You get a chip with a Spanish phone number and a time corresponding to the amount of communication that you have chosen (10 euros, 20 euros ...). Different operators charge about the same price: between 25 and 30 cents per minute. When the card is full, simply recharge online with a European card, by phone, at most local grocery stores or by going directly to a store of your operator.
You can also opt for a package "contracto."
This is the best and most economic way to stay in-touch with friends and family out of the country. You can download the Skype call and talk for free from computer to computer or phone to computer, without limitation, to the world. Also, Whatsapp is the best way to contact people. Because it uses internet, you don't have to waste your SMS messages and you can text people while abroad by using WiFi.
Orange offers two great plans with calls, texts and unlimited, 3G internet.
Delfín allows you 300mins/month of talking to other Spanish numbers, and 500MB/week of high-velocity internet usage (after 500MB, the speed is slower, but still works fine.) for just 20€/month.
Ballena allows you only 100mins/month of talking, but 1GB/week of high-velocity internet for just 22€/month.
Vodaphone also offers some good yearly contracts, which give you a free smartphone for free with contract.
And Yoigo has a new plan that offers 300mins/month of calls and 1GB/month of internet for just 20€/month.
But if you're a fan of music, Movistar has an option to get Spotify Premium for an additional 5€/month, which isn't bad with their 9€/month plan that allows unlimited calls, 500 free texts, and 500MG/month of free high-velocity internet.
If you do not have an internet connection in your new Madrid accommodation, remember that all municipal public libraries offer free internet access for 45 minutes. Remember also to take a look at the library of your university. Most university libraries also offer free internet access. Search for your local library.
Finally, some areas of Madrid, including multiple bars and restaurants have WiFi. Here is a map of places. For example, Starbucks gives you a code with your receipt to access 45 minutes of free WiFi.
Note: All numbers Spanish mobile numbers begin with 6- and landline numbers with 9-...