I don't have any tattoos but I attended a lecture on it as part of my MSc in laser engineering and saw it being done at a hospital. Basically the principle is to fracture the ink into smaller segments that the body can process (the reason tattoos remain is because the skin is unable to 'deal' with the ink and rather than remove it, it just puts a barrier around it and leaves it).
The laser itself is q switched which means it gives out a very short pulse of intense light. The laser does not look like how you might image on James bond but is a rather boring 'block' with a fibre optic cable running into the back which the operator manually scans over the skin. Each 'zap' is about 3mm in diameter and are done so that they overlap each other, so to process a 5cm x 5cm tattoo may need approx 250 zaps.
I'm told the zaps are very painful, like a hot needle and the pictures of the skin immediately after treatment look horrible and very sore. The skin will need at least a week to heal after each treatment and the number of treatments required varies depending on the pigment used as some mentioned above. Typically you will need at least 20 treatments at £100 a go for a 5cm x 5cm tattoo (circa 2007 prices) but may need upto 40.
The success rate depends on the tattoo but some can appear to have almost fully gone whilst others just appear faded and blotchy.
Hope that helps - even if it is hardly good news!