First you need a smartphone or just any feature phne that has internet (3G or GPRS). if you visit a phone dealer they'll explain which ones are "have internet" features. A 3G one is best.
To chat and and do facebook you will need to download an application like fring (
http://www.fring.com/), Nimbuzz (
http://nimbuzz.com/) or ebuddy(
http://www.ebuddy.com/). you just visit any of those sites on your mobile and you'll get a ddownload option. just ownload, install and then add your chat accounts and Facebook and you'l be set.
if you're using Telecel, staying online per day will cost you nothing. If it's Econet, something between 10 and 20 cents per day.