To get to Manuel Antonio you can rent a car, take a public bus in San Jose, or join an organized tour. You can also get to Manuel Antonio by plane from San Jose in 20 minutes.
Next to the National Park there is a parking lot where you can leave your car. You access the park on foot, which is the only way to visit it.
If you are going to visit other destinations in Costa Rica, I recommend leaving Manuel Antonio as one of your last visits. Inside the park you will find plenty of wildlife, and very nice beaches where you can relax and enjoy the Costa Rican sun.