King Charles I enclosed the Game Park at Richmond the best part of four hundred years ago. It was a nice gesture and although they subsequently cut his head off, Londoners retained the park. It's still there, and the deer still amble around, unworried by the huge airliners passing overhead toward Heathrow. Richmond Park is big (big enough to get inconveniently, rather than hopelessly lost). It comprises rolling open ground interspersed with largish wooded areas. Some of these are plantations and one, the Isabella Plantation, is particularly attractive, especially in spring as it contains many Rhodedendron and Azalea bushes. It is planted around a small brook which eventually fills a very pleasing duck pond. Nice spot for a picnic.
Don't forget that Richmond Park is the biggest open space in London but it is not the Serengeti: it has large herds of deer, horseriding, some nice (if sometimes windy) walking, and it a lot of ducks and geese in a number of ponds. It is a pleasing, airy place and a good antidote to too much of The Smoke. There are some lovely views from various points, such as the Pemroke Lodge gardens - but don't expect to see Nature red in tooth and claw. If you like cycling, it's a good spot to go - ditto kite flying, where its exposed position can come in handy. You can hire ponies at the stables by Robin Hood Gate if that's your thing. Or just wander about aimlessly. Some people seem to enjoy just lolling around in the long grass smoking cigarettes on hot summer days. Fat, crooked, odd smelling cigarettes.
You can drive around it in a car, park at Pembroke Lodge and have a cup of tea and a bun, and go for a long bracing walk. It is near Wimbledon Common and you could combine the two in a long and surprisingly rural walk from Richmond railway station to Wimbledon railway station and back into town - country walking in Greater London. The A-Z guide has a good map of the park and of Wimbledon Common. The park is also in striking distance of the National Trust property at Ham House, from where you can walk upriver back to Richmond, and indulge in more tea and buns.
One point - when I say these are rural walks, I am only slightly exaggerating. The paths can be very muddy and the facilities are few and far between. If it rains, you get wet and muddy unless you dress accordingly. And because the park is exposed, I can assure you it is possible to get VERY wet and cold in Richmond Park if you get caught in a storm.