Kinda depends on the time of year. For slower periods, I'd say give yourself 30-45 minutes. By the time you park you will either need to walk or take the tram from the parking lot to the Transportation and Ticket Center (TTC). At the TTC you can catch either the monorail or boat. Note that the monorail only takes maybe 5 minutes to make the trip while the boat is more like 20 minutes.
Once you reach the park, you will have to go through the security bag checks (unless you don't have a single purse, diaper bag, camera case, backpack or fanny pack in your party), and then through the turnstiles. They will let you physically enter the park before 9am, but the different "lands" off of Main street will be roped off until exactly 9am.
Driving you cannot get any closer to the MK than the TTC. Resort busses drop guests off right outside of the turnstiles, but guest vehicles are not permitted that close to the park.
