How would I go about leveling a sagging floor?
There are two ways to fix this.


have the cabinets installed correctly.  They should have been shimmed to at least very close to level.  This is basically a one day job and isn't rocket science.  You unscrew cabinets and shim them.  Front bases have to be redone.  If someone installed these for you I would call that company to come back out.
install plywood over cabinets.  Have it planed/sanded to meet the needs (this will be difficult).