One thing to carry is an ethernet cable, as hotels often have ethernet ports in the rooms.
There usually isn't any trouble receiving mail, but there may be in sending it if the hotel is not using your ISP's server. Usually a call to your ISP will tell you which port number to use for outgoing mail while traveling. This is set in Mail>Preferences>Accounts>Advanced.
For wireless, usually you just turn on the wireless, and if it doesn't find any of your usual wireless networks, you will be asked if you want to join a network that it can find. You can just click on the network and then on "join", providing a password if required.
You can practice this at your local wireless cafe or local wi-fi hot spot.
One precaution--don't do anything sensitive like banking at a popular free hot spot--save that for a more private setting. You don't want someone looking over your shoulder getting passwords, for example. I'm not totally up on what's safe and what isn't, and maybe someone will post some more explicit information, but I'd stick to innocuous things until you know more about what is safe and what is not.
Good luck, and happy traveling!
