It can work in lots of different ways. Open drum breaks are important, you can use loops, or individual hits to play new patterns and create new combinations of sounds. Other sounds work the same way, you can use a loop, or chop things into smaller pieces and put them back together in creative ways.
Lots of Entroducing is based on chopped up drum loops, with other layers of loops and pieces on top. Removing a vocal from a song doesn't work (for the most part), you have to find samples that are either open, or you're forced to find pieces that work as a whole.
It takes lots of patience to find pieces that fit together, pitch is one of the biggest obstacles. There are some methods available now that weren't available when Entroducing was made, for example, Ableton Live software allows you to stretch sounds without affecting pitch. Personally, I still think that only works for small shifts, anything too extreme sounds unnatural.
The most important thing is having a broad base of source material to draw from, a sampler is only as good as what you put in it. The more material you have to draw from, and the better you know the source material, the more articulate you become. In Shadow's case, the source material is old records, but with a sampler, the skies the limit.
I think the best way to learn how to make music by sampling records is to DJ... mixing skills, and an ear for what works come in very handy. I think of my sampler as an automated turntable. If I had eight arms, I wouldn't need a sampler.