Internet access is widely available. Even most of the more remote areas have some type of internet access available. Many larger areas also have WiFi. All of the Camperos chicken/pizza restaurants (which are numerous) offer free WiFi, as well as many other restaurants and cafes. Some hotels may also offer computer banks with internet access. Just ask and you eventually will find some sort of free access.
==== Mobile (3G/GPRS) internet access ====
If you have an internet capable mobile phone such as iPhone, Google Android, Nokia N95 etc or USB dongle for your laptop, you just need a local SIM card (roughly Q25) and can start enjoying the prepaid access plans, which generally come in lots of an hour, a day, or a week.