This should be a simple thing to remember and follow, but I see these used improperly all over the place...
There: [adv] basically indicating a location. There are a few other uses, please see the full listing here.
Their: [poss. adj/pron.] indicating a possession. Details here.
They're: [contr.] a contraction of they are
There, standing with their umbrellas, are four men wondering where they're going to eat lunch.
Not a great literary piece, but hey, it gets the point across.... I hope. Please keep them straight!