There = referring to a place (i.e. "The hotdog stand is over there")
There = used with verb (is, am, are, was, were)...(i.e. There is a new model car out now")
Their = possessive...something belongs to them...(i.e. My kids spill their cereal every morning")
They're = contraction of "They" and "Are" (i.e. "If I don't learn propper grammar they're never going to let me into University")
Unless I work on my grammar, there's (contraction...usage with a verb "Is") no way they're (contraction...they are) going to let me pass the next grade in their (possessive) crummy school.