There is only one way to double tongue easily (unless you are naturally gifted - then you might want to consider a career in politics :), practice intelligently and diligently.
Although there are many arguments about vowel, I advocate using a Tu-Ku pair for beginners.
1. Start by saying these syllables without trumpet or horn using a whisper voice. This is to get the tongue used to the "new" motion. Tongue the trumpet the way you talk. If you have problems in speech, adjust accordingly.
2. Start by practicing the Ku syllable alone. What most people
forget is that you want to make the Ku sound very much like a Tu.
You must be blowing air while using the ku syllable and not let the entire
close off. The motion of the tongue is very quick and decisive. Eventually, you will want to migrate to a Ka and perhaps a Ko syllable, but the Ku will be better at the beginning since it appears to not contribute as much to the throat closing off.
3. Start practicing the pair SLOWLY. You must be able to effectively tongue the pair slowly before speeding up or you may never have full control of the double tongue.
Let the sound be the guide. It should simply sound like fast tonguing and not like another method of tonguing altogether. If the tongue gets excessively tired quick, it may be because you are not moving enough air. A lot of people (myself included) sometimes play like the tongue makes the sound. It doesn't. Vibrating air passing the lips makes the sound. The tongue is only a instantaneous interruption of the airstream.. like a sheet flapping in the breeze (but then we are back to politicians :)
I'm sure many fellow TPINer's will have much to add :)