This is (at least for me) the easiest and cheapest way to fix the home button. I had a Ipod touch 1st Gen which had a broken home button and Apple change it for free, with this second Ipod the home button also broke but I have no longer warranty so I figure out a way to fix it. Hopefully this will work for you too.
Step 1: Cut a Piece of PVC Card
At this point you should find a regular pvc card that you dont use anymore, a bank card or and old school one may do the work. The measures that worked for me are 1.7 x 0.5 cm