What you need is the ability to select just one part of a photo. You'll also want a program that let's you work in Layers. Lightroom and Aperture aren't yet very good at that. Photoshop Elements is a good place to start. PaintShop Pro and Corel Paint would work, too. There's also the Gimp, which is free but of uneven quality.
The general process would be to select the part of the photo you want to keep, then copy it and paste it onto a different background. Each program mentioned has several ways to create selections. The good news is that you can choose the one that makes most sense to you. The bad news is that it's hard to describe all the ways you can go about it.
michael mckee
My Port Townsend – A City in Photographs – 365