One of the easiest ways to explain double strike to newer players is that a creature with double strike has first strike and deals combat damage when other creatures do too. And for the most part, this is an accurate description. It will deal combat damage twice, in the first strike combat damage step and in the normal combat damage step.
However three are some important rules related wrinkles to be aware of where the above quick description does not adequately cover how double strike works. The first and important one is that effects that remove first strike from a creature or specifically refer to first strike will not affect a creature with double strike at all. There are not a lot of cards with abilities like these, but some like Phyrexian Splicer and Talruum Champion will not affect a creature with double strike.
Another thing to keep in mind is that having both first strike and double strike is redundant and won’t do anything more then if it were to just have double strike. There is not a way to have a creature deal combat damage three times in a single combat phase…yet.
Finally, it is possible to give or take away double strike in the combat damage steps. If a creature loses double strike in the first combat damage step, it will not deal combat damage in the second. If there is a first combat damage step and a creature gains double strike at this time it will deal combat damage, but only once in the normal combat damage step.