I'll try to explain がる and がっている more generally, and then conclude with a direct answer about たがる and たがっている.
As stated in When to use 欲しがる instead of 欲しい, it is strange to talk directly about the mental state of someone else. がる provides one medium for discussing your conjecture about another persons mental state, and roughly means "shows signs of X". It is used specifically with ～ほしい, ～たい, and adjectives relating to emotion (often called personal predicates).
たけしさんは食べたがっている。Takeshi is showing signs of wanting to eat.
兄は車をほしがっている。My older brother is showing signs of wanting a car.
彼はうれしがっている。He is showing signs of being happy.
Generally, the difference between がる and がっている resembles the difference between the non-past and ている forms in other verbs.
彼は犬を怖がる。He is afraid of dogs. (generally speaking)
彼は怖がっている。He is afraid. (right now)
It seems that especially with たい and ほしい, がる and がっている can introduce some new subtlety. Consider the following:
車をほしがる。He wants a car.
車をほしがっている。He wants a car.
On the surface, both seem to simply mean that he wants a car. However, there is a little more to it, ほしがる conveys a sense that he wants a car in general, but right now, it may not be his top priority. At the present moment, he's probably showing signs of something else (maybe he looks sad because his test grade was low!). On the other hand, ほしがっている conveys a sense of immediacy and importance. If he ほしがっている's, he is probably either showing signs of it right now or he wants it enough in general that he would ほしがる it pretty often. Regardless of which you choose, at the present point in time, he wants the car.
Here's how you can keep it all straight. Remember the literal translation of がる? "To show signs of wanting"
車をほしがる。He shows signs of wanting a car.
車をほしがっている。He is showing signs of wanting a car.
Disclaimer: My experience with this form is not extensive, and I'm drawing pretty heavily on intuition (from a very modest amount of experience). I hope someone else can make sure I haven't misrepresented anything or left anything out.