Some quick answers...

Originally Posted By zeppelin03
How do people generally go about cleaning the things they use for cooking and the like? Just save a bit of water and rinse them off?
Yes, exactly. Boiling water the next time will kill of any lasting nasties.

Originally Posted By zeppelin03
Also, what about personal hygiene? Do people bring toothpaste and toothbrush.
Yes. From full size toothbrush down to fingertip toothbushhes (toothbrush's? toothbrushi?)

Originally Posted By zeppelin03
Soap for bathing?
No. Baby wipes come in convenient 10 packs, and work well enough for those times you need to get clean.

Originally Posted By zeppelin03
I would assume people at least take toilet paper along.
Hells yes. Though some people go without and do just fine. Not me though.

Originally Posted By zeppelin03
Or do people ruff it completely and bring none of this with them?
Some... just depends on your own personal comfort level.