The two tracks you mentioned may be the closest in ND, but the dragstrip locator says there's a track just across the state line in MN. According to Mapquest it's only a couple miles from Fargo ND!
INTERSTATE DRAGWAYS 2009
It's an NHRA 1/4 mile track. From the website it looks like Trophy is the entry level class. $40 to enter, limited to 11.50 and slower, no gizmos or transbrakes allowed, slicks or street tires are OK. Short of a test and tune session this looks like the best bet for a beginner.
Read up and ask questions, but the only way to really get into it is to go and run. As long as you don't have an atitude you will find almost all racers will go out of their way to help a new guy.
Now for the standard warning. Drag racing can be very addicting. Some people get severly hooked on their first trip. Signs of a drag racing addiction are an always empty wallet and a constant big smile on the face. Don't say I didn't warn you.