you'll need a dial-up ISP number, some high-speed providers also give dial-up access numbers for travelling. Check with your internet provider first. I have Roadrunner and they have several local Orlando numbers that I can use.
If your ISP has dial up numbers, then you just need to bring a laptop and a phone cable to hook up the laptop. You should have either a software the ISP provides or a modem dialer program.
If your high speed ISP doesn't have dial up numbers, then you'll need to get one. Some people use Netzero/Juno. It's free but you only get 10 hours a month, or you can pay $9.95 for a month's access. You can also check around for ISPs that give out free month's trial to use their service. It might be worth it to use those. Or if you have AOL, you can use their numbers.
Either way, you have to have your own numbers to dial up to if you're going to use the dial up internet.
If you stay at a resort that has high-speed internet provided, then all you need is your laptop & a network (ethernet) cable. Or if they have wireless, then a wireless card or the built in wireless that the laptop has. The laptop's network card will find the connection, you don't need to do anything.