So how does this thing work... the whammy bar is pushed towards the body and the bridge is pushed downwards along with the strings? I still don't understand how a trem works...

The Ibanez I may be buying has a locking trem, not an OFR or anything but it looks reliable. I hear Ibanez's trems hold tunings very well. It's going to be my first trem guitar, so I have not much of a clue how to use it, so I'm buying mainly because I need a 2nd and this guitar is cheap(used).