I would give yourself at least a month to register if you have a specific date in your mind.
When you register, you will able to select the date you want as well as time.
I scheduled 10 weeks in advance. When I scheduled I chose a center, and then from a calendar you choose the date you want. I think there are only two times available (I'm not sure): early morning (8am) and early afternoon (12ish).
You should schedule at least a month before if you want a date. You can take the DAT any day, there's like 3-4 time slots per day. I was trying to reschedule my exam up 1 week but the only next open date was 3 weeks ahead, so I have to take it at a different Prometrics like 50 miles away.