any photographic suite that can work with layers will do the job there are a few ,some cheaper than others ,photoshop is the premier photoediting suite , but darned expensive ,coral do one at a fraction of the cost but even that may be more than you would want to spend ,have a look around online (google search ) for photo editing softwares ,find some that is in your price range and check out thier capabilities before you commit .most software sites for photoediting have manuals for thier software and some even have tutorials to show off their abilities . good luck.
If you are going to be a keen photo editor, Photoshop Elements 8 will do an excellent job. There is a bit of a learning curve and it costs about £70 but if you got very keen and wanted a more advanced programme such as PS CS5, your experience with Elements 8 woukd mean a lot less to learn. If you are an occasional user only then the cheaper or free programmes above would be fine. I agree with Procliamer.
Tamsin - you've had several good suggestions above for software.
Here are a couple of tips for doing the job.
When you choose the image that you want to cut out and paste into another photo, in order to make it believable, you need to pay particular attention to the lighting. Try and makes sure that the direction and quality of the light is the same in both photos.
And when you've created a marquee (ie: a mask/selection) around the image you want to cut out, before you cut it apply some feathering. In Photoshop you'll find this function on the Select menu, listed as Feather or Refine Edge. Without a little feathering, your cutout will look hard-edged and unreal.