Is the hardware certified to work with a 64 bit OS? Do you have a 64-bit processor?
You will have to buy a 64 bit version of the OS and install that. To the best of my knowledge you cannot simply upgrade from an x86 version of Windows. That means you'll have to reinstall all your programs, drivers, etc.
Installing a Windows OS is not very difficult, but it can take a while. There are plenty of walk-through tutorials on the net with screenshots if you need them.
The biggest problem you'll most likely run into with a 64 bit OS is finding drivers for everything. You have to get drivers specifically written for a 64 bit OS for your hardware. Also you will want to check whether the software you use has 64 bit versions available to take advantage of the architecture.
All new laptops should run 64-bit versions of Windows just fine - I run Win XP Pro 64-bit (which is actually a cut down version of Windows Server 2003, just named XP Pro) on around 8 computers and it is very good.
It only makes sense to go 64-bit if you have got over 3 GB of RAM or more though. Driver support seems to be pretty good, but you will have to take into account the fact that XP is being phased out even though Vista is not particularly successful so I think Windows XP (including 64 bit version, which is actually newer) is going to remain with us for a long time.
P.S. Forgot to add - you can't "upgrade" OS to 64-bit really, you will be effectively doing reinstall. I am not sure about license issues like whether it is possible to swap 32-bit license for 64-bit, it might have been possible at some point though.
[edited by: Lord_Majestic at 1:50 am (utc) on Feb. 5, 2008]
You can download a time-limited 64bit version of XP. You can install it next to a 32bit XP installation and dual boot (i.e. a menu is displayed at bootup and you choose which one to run). You cannot easily install it next to an existing version of Vista (but it can be done).
I can't remember if you can upgrade to a paid-for version when the trial runs out but at least you'll know if it all works.