The first thing you need to check is whether the strings are simply slipping because they have not been put through the hole in the post and wound on very securely. When you turn the key, does the post go round? If it does, try restringing before anything else. Sometimes, the screw that holds the cog onto the the post comes loose and the cog drops off. This is easy to spot unless the unit is sealed! If the post doesn't go round, this could be the problem - or the actual button you turn to tune may have come loose. Most of these things are easy and cheap to fix. In the 'worst case' scenario, the two tuners (aka 'machine heads' are so worn or damaged they need replacing. Your local guitar shop is the place to head for.
Simon Croft, June 2010