Mainly what I do with a 3 string is use the 1st string only for slide. So you would go up and down one string to make your melody, as if it were a one string diddley bow - not across the strings. If I bring in the other strings they are more or less like a drone that repeats the 1st string. I also include the open string note and the octave note (at half the string length) for variety or special effects.
That being said, there are also a few nice bluesy licks down on the lower end of the scale that go across two or three strings.
Adding some vibrato gives slide playing a really nice singing quality.
Check out my really basic beginner's slide video here:
Keni Lee Burgess has extensive instruction materials for playing on a CBG. I haven't personally used any of his material, but it's supposed to be good stuff.
Shane Speal has also posted several free CBG playing lessons online. I found the one on picking patterns very helpful.
Shane also likes to use a stubby slide, which can be used on the middle or bottom string without activating the other strings. This would open up further licks for slide.