Start with the datasheet for the gates used:
http://www.mouser.com/ds/2/149/NC7SV58-196469.pdfwhich explains how they can be configured as a range of simple 2 input gates, and also the PCB layouts from the kickstarter project, which will let you trace from the jumpers to the inputs of the actual gates.
The pin duplication at each end is so its easy to jumper any single one of the three inputs to either Vcc (PWR) for logic '1' or Gnd for logic '0'. It also lets you feed more than one gate from the Y output of the previous one - either daisychain using the pair of pins for each input or simply wire both using the pair of pins for the single Y output.
What to do with them? Well there isn't a lot you can do because you've only got 10 of each type, the odds are you'd run out of one type before you'd used all of the other type, and they are only very basic two input gates. If you want one combination of four inputs to produce a specific output and all other combinations to produce an opposite output, that's three used up right there. A S-R flipflop would take two of them. A clocked J-K flipflop would take six of them.
For comparison a 74HC138 can be used to select any single combo of four inputs to produce an active low output (and 74HC238 for active high output) and you can get several for a dollar.
They *MAY* be useful to the Arduino maker scene - or at least that subset of it that are scared of breadboards, real components and even soldering - when they need to flip or combine signals to patch together interfacing some breakout board, but otherwise they are very much a toy.
To figure out what to do with them, if you've got a windows PC, you may find Logic Friday useful. Its a GUI frontend for the
Espresso logic minimizer The original website's gone to domain parking, but it can still be accessed, including downloading the intaller,
[here] at the Internet Archive.