I arranged for a car & driver through Patriarshy Dom Tours. They offer a wide varierty of tours in Moscow (with a good reputation) and will also help to arrange guides, cars and other items in St. Petersburg.
The driver, Natasha, spoke little English, but I had written our destinations in Cyrillic, and we made out just fine. She was prompt, polite and even pointed out other buildings to us as we drove.
The cost was $12 US per hour, so we paid almost $100 for the day, plus tip. It's not at all inexpensive, but was well-suited for our purposes.
The easy way to get here is by taxi or those minibuses service they have from St Petersburg. Not very comfortable and very crowded but useful.
Another easy way to get here is by train. The train station stop is just across the entry to the park so it should be very easy.
Well, that is not exactly the way to get here, but maybe to get around, I notice some were riding horses around the park.