You can put 12VDC into the arduino but it may heat up the onboard regulator past it's limitations--depending on what loads the Arduino is supplying.
Stepping DC down from 12 to 9 or 6 can be done a few different ways
an LM7809 can provide regulated 9 VDC
an LM7806 can provide regulated 6 VDC
an LM7805 can provide regulated 5 VDC (but i'm not sure if you should but 5 VDC into the arduino as it's onboard regulator may chop that down--these regulators tend to require 2 volts above the regulated value.
I've used these in the past and they work fine--and super simple to install. But are only good for around 1 amp. Depending on the load you will probably need a heat sink. Mine alwasy seem to get pretty warm as efficiency is not that great.
Another approach are buck converters. super high efficiency, need no heat sinks, are adjustable and can provide much higher current. I've started using these and the seem to work very well
Hope this helps.