Entering and leaving Ko Samui is generally very straightforward and is not overly bureaucratic, especially considering the huge volume of tourist traffic that passes through.
Citizens of 62 countries, including Australia, Canada, New Zealand, South Africa, the UK and the USA can stay in Thailand for 30 days without a visa. If you plan to stay more than 30 days, you will need to apply for a 60-day visa. See the website of the Ministry of Foreign Affairs (www.mfa.go.th) for more information.
The new Immigration Office is located south of Rte 4169 in Mae Nam. Officials here tend to issue the minimum rather than maximum visa extensions. It's better located and bigger than the former offices in Na Thon, but you may still be denied an extension for no particular reason.
Don't overlook the option to join a three-month to one-year Thai language course with a school on the island, which would qualify you for a student visa to cover the length of the course.