Well, when I went to Khao Yai I went with friends that had a car. I'm not sure how a traveler would get around in the park after you arrive at the main gate. Bicycle would be good. Or possibly hitchhike. We actually did hitchhike one day as our hike ended up on the road quite some distance from where we left the car and a guy with a pick up truck let us climb in the back.
There are plenty of signs showing you where every thing is at once your in the park. Hiking trails, Water Falls, distances and other interesting stuff!
The way we got around the park was in an open-air truck. It has bench like seats on each side. They did have some padding so the ride wasn't that bad. If it was raining it wasn't that great.
This is the transportation that goes around the National Park. The driver will take you to the far routes around and it will cost you around 10baht or so. I've seen a couple of farang hikers riding.