The pentatonic scale is a great vehicle for moving outside. It has a very clear structure and sound which the listener is familiar with. Due to its simplicity and familiarity, you can get away with playing it, even if it does not fit the harmony in a traditional sense.
The first thing I experimented with when I got into playing outside was "side-stepping", i.e. shifting the pentatonic scale up or down by a half-step. Here I think it's important to avoid the most tempting thing, which is simply repeat a phrase a half step lower or higher. Instead, what I practiced was moving down when I actually played the pentatonic scale half a tone higher, and moving up when I used the scale half a tone lower. To give a very simple example, if you play in C major pentatonic, instead of playing
C D E (inside) C# D# E# (outside)
I would try something like
C D E (inside) D# C# A# (outside)
The most important thing is the way you get outside and - probably even more important - the way you get back inside. I've come to the conclusion that as long as you get these two steps right, anything goes.
Other pentatonic scales that I've found to work well are the scales a minor third up, and a tritone up (or down, which is the same). But just experiment and trust your ears.
I've transcribed (guitar tabs) and played an example of Chick Corea playing outside here. In this example, he also uses the pentatonic scale to go outside.
Another good tool for playing outside is the whole-tone scale. It also has an obvious inherent logic to it, which helps make your lines sound smooth and musical, even though the individual notes may be totally off. One example I always teach my (more advanced) students is the use of the whole tone scale when playing in dorian. Let's say we're in C dorian, then you'd have the following whole tone sequence inside the scale:
Eb F G A
The trick is now to continue this sequence using the whole tone scale, which means going outside of C dorian:
Eb F G A B C# D#/Eb
and with the last note (D#/Eb) we're magically back inside C dorian.
There are many more interesting concepts for playing outside, but I think the only way to really learn it is to analyze and learn solos of good players who use this concept, and to develop your ears, so you can hear and find on your instrument what you want to play.