The mobile network 3G/GPRS/GSM covers the whole city. If you are coming from a non-GSM standard country check your mobile phone for GSM compatibility.
To get a phone you usually need to succumb to the German love of registering and paperwork. The anmeldung (registration) is necessary for practically everything, including buying a phone. The process is short, but you will need to bring a rental agreement to your local Burgeramt. Choose the area closest to you and then click on the office. Click on "Termin buchen", which means "Book appointment" to choose day and time. You will also need to supply your passport.
Phones can be purchased from any of the electronic stores like Saturn or MediaMarkt, phone stores, and even some grocery stores like Kaufland. Basic phones can be purchased for as cheaply as 8 euro, but more expensive phones have much better features. SIM cards can also be purchased at these stores for around 10 euro.
Different companies offer different rates, so shop around. If there is a specific country you will be calling, investigate which companies offer the best rates. Calling a landline is much less expensive than calling a mobile. Expect to pay between 0.279 - .49 euro to call mobiles, and 0.079 - .49 euro.
Contracts are usually for 24-months and charge a monthly fee and package. These offer a better deal per minute than a pay-as-you-go phone. Contracts are usually in German, so if you are not comfortable in German make sure to bring someone who is. It is your responsibility to understand all aspects of a contract before signing.
Some contracts are extremely difficult to cancel. They may require you to prove that you have left the country by sending them your registration outside of Germany. Know your cancellation terms upon signing.
Pay as you go phones can be purchased from electronic stores like Saturn or MediaMarkt. They can be as inexpensive as 8 euro and come with a small credit (usually 1 euro). Expect to pay between 20-30 in general.
You can also buy a second-hand phone that saves some paperwork and can offer a good deal. There are stores off of Karl-Marx strasse in Neukoelln, but your best chance is online. Look on ebay, Craigslist, or EasyExpat's classified's.