How to rebuild a Li Ion laptop battery?

Typically, the batteries are connected to each other via spot welded tabs. You could solder wires to the batteries you found, but it might not fit afterwards. Make sure you use a wire with enough current carrying capacity (i.e. 14 AWG). Theses batteries do get hot and pass a lot of current during peak loads. You can also build yourself a spot welder rather cheaply if you want to try this route.

Make sure the case is well closed after your repair. Epoxy should do the trick.

There are a few tutorials on the web as well.

Beware: Soldering Li-ion cells can be somewhat dangerous, as when they get hot such as during soldering they can tend to explode.

Unless you have experience with electronics and soldering I wouldn't risk it. Batteries put together incorrectly have an unhealty disposition to extreme exothermic reactions (i.e. blow up) which can be quite fatal if you are close.