When traveling to Thailand, it's important to have the right visa so as not to land in hot water with Immigration. Forget anything you've heard about bribes and under-the-table deals, when it comes to your visa, do not treat it like you would a T-shirt from a street seller. Phuket has an international airport and there are also ferry links.
Thailand offers most countries a visa on arrival. If you are arriving by plane, such as at Phuket International Airport, then you will be given 30 days for the purpose of tourism. You can not work on this visa.
If you are arriving into Thailand over land (not possible in Phuket) then, thanks to the new Immigration laws, you will only be given a 15-day visa on arrival. This can be a pain for travelers looking to stay in Thailand for more than a couple of weeks.
Officers at some land borders will ask to see documents for your next journey to make sure you will not be staying too long. Likewise, some airlines will ask to see your oncoming travel documents before they even let you on a plane to Phuket. This can be frustrating if you're plans are not set in stone, but it can be worth buying a cheap air ticket from one of the Thai airlines. Dates can usually be changed without incurring an extra charge.
The most sensible thing to do for any tourist hoping to spend some time in Phuket is to buy a tourist visa from a Thai consular office outside of Thailand. These visas usually give you 60 days with the possibility to extend for another 30 days at any Thai Immigration office. This saves the hassle of running out of days and having to do a visa run. Again, however, you can not work on a tourist visa and nor can you change its status to a non-immigrant visa. To get a non-im visa you have to leave the country and go to a Thai consular office.
Another recently introduced Thai Immigration law states that tourists can not be in the country for more than 90 days during any 180-day period. This means that from your first date of entry, you can only be in the country for 90 out of the proceeding 180 days. Enter Phuket on January 1 and stay for three months and you'll then have to leave for three months and will not be able to return until the end of June.
Whatever you do, do not overstay your visa, as you can get into all sorts of trouble and you'll just end up wasting money on fines.