I just put together my Crack/Speedball recently so I know which tools you're going to need and some tips for the process.
You're going to need a couple of tools...
Solder
Solder Wire
Solder Tip Cleaner
Very small pointed pliers (the smaller the better to get those wires wrapped around those terminals easier)
Very small wire clippers (to cut wires and to remove excess wire after soldering, the smaller the better)
Wire stripper
Solder sucker (you're going to need it if you haven't soldered before)
Screw driver for small screws
Helping hands (to hold Speedball PC boards while you solder in the parts)
Important: After you're done assembling it you're definitely going to need a voltmeter to make sure all the connections are good.
Also, make sure you have all the bands for your resistors, rectifiers, etc. pointed towards the proper side or it won't run properly!
I would suggest practicing soldering a few times before applying it on the Crack. Just take your time, follow the directions to a T, and you should be good.
Good luck with your build and all the best Kyno!