Chris Blattman points to and offers some safari tips. Sounds like most of his experience is in visiting the East Africa parks so I'll offer a few general tips from my own experiences in Southern Africa parks - Botswana, Zimbabwe and South Africa - and trying to do things on a shoe string budget.
1. Camp in the parks when at all possible. In Botswana this is relatively easy to do - contact the Tourism Board and they will get you started, just make reservations early -especially if you are living on the continent as you can most likely borrow all the gear you would need (tents, stoves, water jugs, cooking gear, etc.) from friends and acquaintances. If you are doing the tourist thing you can rent gear and still come out cheaper than staying at a lodge. You have never camped until you have camped in the middle of the African bush. There are few experiences that will make you feel as alive as lying on your back in the middle of the night with a herd of elephants passing almost silently through your campground or a couple of lions chasing an impala through your evening meal. A couple of hints:
A. If you're in Botswana make an effort to camp in Deception Valley, Savuti, Linyati and Kasane.B. Take very seriously all the precautions/instructions you will read and bring extra everything.C. Bring a headlamp.D. Spend the night before you leave in the nicest lodge you can afford - eat a great meal, take a hot shower and sleep in a comfortable bed.E. Insider Tip: If you don't want to/aren't able to camp but don't have money for the lodges try calling around to a boarding school in a nearby village. If the students are out on holiday most will rent you space to sleep in and let you use their showers/bathrooms - you may even get lucky and there could be an empty staff apartment. You'll probably still need to bring along a propane stove for cooking but those are easy to find. This can save you a ton of money. Oh, don't leave anything of value, real or perceived, around during the day.
2. As Chris suggested, drive yourself if possible, but make sure you buy a good, current map of the park and have a little experience with 4-wheel drive. Swap information about what you have seen and were you saw it with the other drivers you see - the pro's may be a little icy at first, after all you are a lost customer, but if you share the goods first they usually come around. The military/anti-poaching forces are another great source of info - they are usually hanging around the gates and smokes are appreciated.
3. In the heat of the day most everything is asleep and you should be too. Save your energy for very early mornings - in the truck at first light - and late afternoons.
4. Bring a good book.
3. Buy a nice field guide. It doesn't take long to get excited about the animals you are seeing and want to learn more about their habits. In addition, it will help you notice and appreciate all the amazing lesser known animals, especially birds, that are also present. Plus someone can read aloud during the long stretches of seeing nothing.
4. Take a lot of pictures. Most will be worthless but a few will be amazing.
5. Bring a lot of water, sunscreen, a good hat and sunglasses.
6. If you are living and working in country bring along one of your national friends. Most have never been able to experience the heart of their national animal resources in this way - and, unfortunately we're quickly pricing them out of the market - especially those from urban areas.