Shoot it in the head with a BB gun, decapitation, your pet dogs or cats (if you have any), and then theres always a heavy rock, or rat traps. You can place them in locations that you'll remember and check them daily.
Um.... Try a mousetrap? If you can, maybe get a larger-than-normal mousetrap for a rat. Would that be called a... rat-trap...? (No sarcasm, I really don't know.) You would, of course, want to set up multiple traps. I've also heard of enclosed mousetraps that have a door that shuts when they go off, and odor control. Plus, you never have to see whatever it is that got caught. Again, you might need a large one for a rat. As for knowing exactly when it dies, unless you rig up some contraption to make the trap text you when it goes off, I don't think it's possible. Just check all the traps once or twice a day.