Phones and internet
There are lots of providers for phone and broadband internet (see http://www.meinestadt.de/goettingen/dsl). They all have different packages and contract requirements and not all are available in all areas, so please check. Most internet services come with a phone option as well, saving you the trouble of arranging that separately, and some can even bundle mobile phone service in, too. Many of the largest providers have storefronts in Göttingen where you can go for information, otherwise ask friends and colleagues what they recommend, and/or search online.
Mobile phones/cell phones
Mobile phones are very widely used in Germany, and are rather peculiarly called Handy. Be cautious when you sign a contract: Some of them contain hidden charges or conditions. Also many contracts are automatically renewed at the end of their term unless they are cancelled in writing a minimum length of time (e.g. three months) before the end, so make sure to read the fine print. Also, make sure you know what charges will apply if you exceed the included number of minutes, if a flat rate for the internet is included etc. If you will not be in Germany for two years or you do not want the hassle of a contract, most providers offer a prepaid option. For this you can either buy a phone from the provider or use your own (as long as it is not SIM-locked), in which case you just need to buy a SIM card from the provider of your choice. Prepaid cards (Guthabenkarte) are available in many supermarkets, kiosks and other shops.
Local phone books and yellow pages
Local phone books and yellow pages (Gelbe Seiten) are available free of charge at every post office.