mobile phones
Outgoing calls and texting work on most networks. However, it is worth buying a local sim card from one of the mobile phone shops. These are much cheaper around 1/5th of the normal roaming charges, and they will accept incoming calls.
There is no GPRS. the 3G service has recently been started so you can send picture messaging.
Libya's phones are all unlocked, so the locals will not understand that the local sims will not work in all phones. Therefore, it is worth taking an unlocked phone or, when asking to buy a phone, hide yours, so they won't try to sell you a sim.
Sim cards are about USD5 [Correction: in April 2012 it was impossible to find a sim for under 80USD], and phones around USD50.
internet access
There are internet cafes available; ADSL and WiMax internet are now available.