Take croatian A1 highway which connects Zagreb and Split (and goes further down south too, Ploce, Dubrovnik...).
Take the exit towards Gornja Ploča, Plitvička jezera, Korenica, Udbina. Pass by Jošan and follow signs to Plitvice lakes. The road is well marked. It will take you about 45 mins-1 hour form highway exit to center of Plitvice.
Plitvice lakes national park is located aproximately halfway between Zagreb and the coast, making it an ideal stop and easily reachable from both destinations.
State road D1 runs through the park and on both entrances there are large car parks where you can leave your car and continue on foot.
Note that the new A1 highway (Zagreb - Split) does not run through Plitvice - if you want to visit it, coming from Zagreb, exit the highway in Karlovac and continue along the D1.
From Zagreb it's about 2 hours drive to Plitvice, same from Zadar and somewhat longer from Split.
Along with several hundred German motorcyclists, we arrived at Plitvice Lakes National Park via Croatia's Highway 1, which runs from Zagreb all the way to Split. This road goes right through the park.