Double tonguing is a difficult and advanced technique, but is very important. It allows you to tongue very fast passages much more easily. Here is some of the first steps to take when learning to double tongue.
1. Find the syllables that work for you.
I use tu-ku, but there are other options such as ta-ka, da-ga, du-gu. First try without the trumpet.
2. Try it slowly on the trumpet.
Using a middle range note, (I find that F works well) try it slowly. You should be able to hear a definite difference between the two syllables. If you are struggling with the ku syllable try just ku tonguing.
3. If possible get a teacher to listen to you.
It is important to know whether you have the correct technique so, if possible, find a teacher or an advanced player to listen to you double tongue. If this is not available to you search for example videos on Youtube.
4. Gradually speed it up.
Using a metronome, start tonguing at a very slow speed. Gradually speed the metronome up until you reach a speed at which you can no longer double tongue. Make a note of this speed. Work on this every time you practice and gradually you should be able to increase the speed at which you can double tongue.
5. Try lots of different exercises.
If you don't have an Arban or similar, here are some exercises that I have found online:
http://www.ultrapureoils.com/media/23605/tonguing_exercises.pdf. This is also a very good video:
http://www.youtube.com/watch?v=4vIb0DjDdN8
