Leonard,
The application period is in early June. Daxter is correct in that they only allocate 1% of tags to nonresidents. Residents can usually draw any hunt by 5 or six years--in part because they exponentially amplify (cube) the bonus points after 4 years. Unfortunately, they really do not provide information about draw odds for non-residents. I really don't know how long it takes to draw a non-res permit in the better units (mostly near Theodore Roosevelt National Park). Although everybody that applies has a chance to draw, you really need to apply for at least four or five years to get your points amplified by the exponent of 3. You must front the $180 tag fee to apply but they refund all but $3 to apply--that is one of the most reasonable non-res tag fees that I know of.
There are some good public land hunts, but much of it is checkerboard. You can hunt anything that is not posted, but I would guess that most of the better private areas are posted.
I have been applying in ND for three or four years--mostly because I grew up there and would like a chance to the hunt mule deer in the region. I have never seen or heard of any real monster mule deer bucks comming out of ND--but those NoDaks keep a pretty low profile.