Hi, I'm Dr. Bonk. I'm sorry to hear about Ceasar's troubles. Depending on the degree of dysplasia, hip dysplasia can be managed. First of all, his activity level should be managed as tolerated, meaning let him do as much or as little as he wants. Try to avoid strenuous exercise such as jumping or running for prolonged periods. Swimming is a great exercise as it takes the weight off those joints and allows muscle conditioning without the the concussion.
It is very important to maintain a healthy weight. Excess weight applies more pressure on painful joints, keep him trim by regulating his food and through exercise.
You can also start giving him joint supplements such as glucosamine chondrotin. These help to support healthy joint fluid and cartilage to keep inflammation down.
You should also have an anti-inflammatory on hand for days when he is sore. Some good ones meant for dogs are Previcox, Rimadyl or Metacam. These are all prescription so they would have to come from your vet. Aspirin works too if in a pinch, but is not recommended for long term or repeated use.
You can also do passive range of motion exercises. These just help relieve joint stiffness without the concussion of running or walking. There are some good videos on YouTube on how to do these exercises.
I hope this helps. Please contact me with any further questions you may have. Thank you and good luck!