Why Is Your Tarantula Lying On Their Back?
First of all, if you find your pet tarantula lying on their back it is very important that you do not touch them as they are extremely fragile at this time. It can be quite alarming to find your tarantula lying in this seemingly unnatural position but chances are it is simply because they are beginning to molt. Most tarantulas will molt while laying on their backs (though some will molt on their sides). Molting usually takes a few hours so keep an eye on your tarantula (remember to not touch them) and within a few hours you should be able to verify it they were molting by the evidence they have left behind in the form of the molt. 
Many people think that if their tarantula is on his back it means they are trying to die. This is not the case and it is quite rare that a tarantula would ever be found dead upside down. They are more likely to be found dead with their legs curled under them then to be lying on their back.

Other Signs That a Tarantula is About to Molt
There are other, more subtle signs that a tarantula is about to molt although some of these can occur for other reasons besides molting.

• Decrease in appetite - A tarantula getting ready for a molt will usually stop eating, sometimes for as long as a few weeks before a molt.
• Decrease in activity - A tarantula getting ready to molt will often become very slow and sluggish.
• Development of a bald spot - Tarantulas also sometimes develop a bald spot on their abdomen that grows increasingly darker as the molt draws near (a bald spot can also occur in New World tarantulas that have been kicking off their urticating hairs). After molting, the bald spot will be gone.
• Increased use of webbing (they may make a mat out of silk for molting).

Dull coloration
If you notice the signs that a molt is impending, make sure the humidity in the tank is ideal and the temperatures are right for your specific kind of tarantula. The proper environment is important for a successful molt. Also, make sure there is no uneaten prey in the tank as even a cricket can seriously injure a molting tarantula.

Molting is Stressful and Dangerous for Tarantulas
As the old exoskeleton is shed the tarantula's body will be soft and extremely vulnerable. Though the actual molting usually takes a few hours, the tarantula's body will be soft and vulnerable for several days before the new exoskeleton completely hardens. For this reason alone you should never handle a molting tarantula. As mentioned before, also make sure there are no crickets in the tarantula's tank and do not feed a newly molted tarantula for at least a week (to prevent new crickets from biting your tarantula before the exoskeleton has time to harden). The newly molted tarantula is so sensitive that even an innocuous little cricket can cause serious harm to them.

How Often Do Tarantulas Molt?
Because spiders have an exoskeleton they must shed the old exoskeleton and form a new one in order to grow. Therefore, young growing spiders will molt more frequently (up to once a month) than older spiders (who may only molt every year or two).

 From: http://exoticpets.about.com/od/tarantulas/f/moltingtarantul.htm