It is most easy to take a tour from the nearby town of Tissa Tissamaharama. You can take a tour from any number of guest house/hotels in the city. Most leave at 5:00 or 14:30, but it depends on if you are going for half/full day or overnight. The entrance to the park is about 3,500 rupees, but it changes often. The tours should cost about 4,000 to 6,000 on top of the admission ticket. It is usually split between the people in the truck, but you should negotiate this. It can be expensive to do alone, so it is best to try and partner with others to increase bargaining power. The tour guides often will use you as bait for people coming off buses. It makes both your lives easier to meet the people off the buses right away, as it gets competitive and most drivers will call their friends to tell them you are coming. They all know what travelers are coming here for.
It is also possible to stay at a bungalow more near the park, but it may cost more and is a little more difficult to reach alone.
It used to be possible to enter the park from Katharagama, but that entrance is currently closed.