What is Gimp?
Gimp, (or The Gimp to give it it's proper title) is a freely distributed piece of software suitable for such tasks as photo retouching, image composition and image authoring. It was originally designed for Linux/Unix but is also available for both Mac OS and Windows. For more information about what features Gimp offers take a look at About the Gimp. It suffers from some usability issues, and many people say that it isn't as usable as Photoshop, however, these barriers can be easily overcome.
More information, and download instructions can be found at gimp.org.
More information, and download instructions can be found here.
More information on the Mac version of Gimp can be read at MacGimp.org, and it appears you can order a CD from there as well.
There is a useful User Manual for Gimo users which can be bought from Amazon.
Grokking the Gimp is a pretty complete manual which can be read online or bought from Amazon as a hard copy. It provides helpful information on all of the standard tools provided, and makes good use of photographs to illustrate the points.
Techniques and help
Red Eye Reduction
Little is more annoying than looking at a great portrait which suffers from red eye. This helpful tutorial by Eric Jeschke is easy to follow and should help rescue the photo. Carol Spears has also authored a tutorial to remove red eye which is available here.
Converting to Black and White
Okay, so everyone knows how to convert an image to greyscale, but that always seems to result in very flat images. There is a tutorial by Eric Jeschke discussing the different methods. There is also some helpful, but very technical, information provided in Grokking the Gimp.
Converting to Sepia
Changing a photo to sepia, allows you to create imagery that has that old look. Again, Eric Jeschke has provided a very thorough and easy to follow tutorial.
Simulating IR Photography
Some digital cameras aren't great at Infra Red photography, even if you do use the appropriate filters. So, the only way to produce these types of image is by manipulation. Eric Jeschke has provided another good tutorial to help this.
Simulating film Grain
Sometimes, especially when working with Sepia or Black and White images the addition of some grain makes the image look more realistic. Eric Jeschke provides another useful tutorial to explain how to achieve relasistic looking grain. There is also a tutorial by Eric Kidd here which also covers this subject.
Reducing Noise in digital images
In some circumstances, for instant low light shots, or at high ISO speeds an amount of noise can creep into your digital imagery. Eric Jeschke has provided a tutorial aimed at helping to clean up your low light noisy images as well as one for more general noise removal (such as for high ISO speeds). Atte Andre Jensen has also produced a tutorial to cover this subject, available here which uses the Gaussian Blur tool.
Altering the background of an image
Sometimes the background of an image can be distracting, and so the mask tools can be used to remove or blur the image. Eric Jeschke has a few tutorials to help in this, one is Replacing the Background, another is Selective colourisation and a third is Simulating Depth of Field.
Generating a lightening effect
The Gimp User Group has a series of tutorials which are mainly related to the artistic side of Gimp, however this one just may come in handy.
Generating a fog effect
Another one from the Gimp User Group, this one explains how to generate a fog to add atmosphere to your images.
Photo touch up and Enhancement
A simple tutorial demonstrating the different ways of enhancing a photograph.
Sometimes when taking photographs it is almost impossible to create the photo you want without overexposing or underexposing the different parts. One solution is to take multiple images from the exact same spot, each metered to a different spot. Then, you just need to combine those images. Eric Jeschke has a tutorial explaining this in detail.
As with most things, there is a lot of information available on the web for Gimp manipulation, admittedly not as much as for Photoshop, but they are around. A good starting point might be this list of tutorials.