In general the high speed connections will be wireless, you will therefore need to have some kind of wireless setup on the laptop (built in, usb adaptor or PCMCIA card).
If you need to add the hardware then it is worth checking with the hotels as some will rent you a wireless card (or occasionally a usb adaptor).
The dial up connection is another matter entirely, for this you will need a modem which you probably have built in, however it's the service provider who will be the issue.
As far as I am aware, for consumers, it is AOL who can provide 'roaming' access - the ability to dial up from other countries. They do unfortunately insist that you have been a member for at least 3 months in the UK before roaming is activated, they refuse to budge on this as I have tried in the past. The other option would be to try and set up with a US provider temporarily whilst you are there, I have not tried this myself so could not comment on its feasibility.
The best option by far is the wireless high speed access, if you do use this method then also install a program such a Callserve. This will enable you to make telephone calls back to the UK for about 3p per minute over the connection, this will save you a lot of money on hotel phone calls.