Many packages available, including:
Serif PhotoPlus - old versions sometimes advertised free
PaintShopPro - sometimes available on cover discs
Picasa - free from Google. Click here.
Adobe Photoshop - the industry standard - about £500
Adobe Photoshop Elements - a cut down version of Photoshop for home use - about £60
Various packages supplied with cameras
All have all the facilities you will need to start.
If you already have software (probably supplied with your camera, scanner or printer) probably best to stick with it initially. Only change if you know you want something more advanced.
If you have no software Photoshop Elements is probably the best. It has most of the facilities of the full package that will ever be needed by amateurs and is the one used by most digital photography magazines.
This course uses Photoshop Elements V4.
Other software will have most of the same facilities but may look a little different and may use slightly different terminology.