It's generally known as a "Fake Book". Meaning it should give you enough information to "fake your way" through the song at a birthday party or something.
Also the chords are usually in Jazz-Guitar syntax. It's similar to figured-bass. But you're not going to see G 6/4 or any thing like that. A G6 has an E as well as a D. A 'sus 2' has a 2 instead of a 3. Same with 'sus 4': no 3. If it says 'add 9', do that: just add a 9. But if it says just G9, you need a flat 7 in there too (Jazz chords often just keep adding thirds off of the triad, so G11 has a flat 7 and a 9 picked up along the way).
[ This is why you'll hear guitar players say: "Don't play a 6/9, play a 13-no-11!" It's because you have to drop the 5 anyway because you run out of fingers! This bit may not be "good advice" but my experience is that you can "get away with it". As @Gauthier has commented, this way of looking at it doean't give you the right seventh. ]
A chord like C/G is a second inversion: it's a C with a G at the bottom. A/G is an A7 in third inversion. These are usually indications of a moving bass-line. The bass needs to lead the harmony into the next chord.
There should also be a chapter or at least a pattern index of ideas for the left hand. Otherwise the book is really leaving you hanging. Off-hand some ideas are: block-chords on the eighth notes (Jerry Lewis boogie-woogie), simple Mozart arpeggios, broken chords as accents (pretend to be cymbal crashes). There's a great book called Boogie-Woogie Hanon that's an excellent resource for left-hand blues-rock patterns.