internet
Internet cafes in Azerbaijan are called "internet klubs" and they are found throughout Baku. Some coffee houses provide wireless internet, but they are quite rare in Baku. Recently public wi-fi service was implemented the central areas. One "klub" with fast internet downtown is VIP, U.Bunyadzade 3. They also have a lot of games you can play.
talk
English and Russian are spoken in many places throughout Baku, but it wise to still either bring an Azeri phrase book and/or brush up on your Azeri/Turkish/Russian before arriving. However, about 80% of population at least understands Russian, and about half the people under the age of 35 will speak at least a little English.
English is well catered for in most shops, restaurants and bars as a result of 15+ years of expats from the oil industry. Very easy to make yourself understood with little local language skills.
See also:
Azerbaijani phrasebook
Turkish phrasebook
Russian phrasebook
post office
Azerbaijan Post locations are dispersed throughout Baku. Mailing an international letter generally costs 0.8AZN.
emergency contact numbers
Ambulance: 103
Fire: 101
Gas Emergency 104
Speaking Clock 106
Police: 102
You must speak in Azeri, Turkish or Russian to communicate your needs. It would be a good idea to memorize key phrases before coming to Azerbaijan - see the Talk section for phrasebooks.