Patellar tendon pain is the pain in the tendon just bellow the kneecap. If you have knee pain somewhere else then it's probably not the patellar tendon that is hurting. The patellar tendon connects your shin bone to the patella, and the quadriceps tendon connects your patella to your front thigh muscles. So your patellar tendon indirectly connects your shin bone and your front thigh muscles. These muscles are large and hold your weight when you squat or jump and you can particularly feel them when walking downhill. So in the end your small patellar tendons take a huge load, and can get hurt fairly easily from running or jumping.
The patellar tendon is located right bellow your kneecap. This tendon connects the bottom part of your patella to the shin bone. If you have pain near your kneecap, but not in this tendon, then it's something that's hurting. Tendons are made of collagen, just like ligaments. The difference is that tendons connect bone to muscle, while ligaments connect bone to bone. Tendons function is to transmit forces between the bones and the muscles they connect. Tendons respond to increasing mechanical load by growing stronger. However if the load increases too fast, they can get inflamed or can rupture.
To put it simply, your patella tendons probably hurt from overuse. The overuse can be a long term (chronic) or short term (acute) overuse. To fix the tendon pain you first have to stop the overuse, give the tendon time to heal, strengthen it with training and start to use it as normal again. Fortunately tendons, similar to bones can rebuild themselves, you just have to give them a bit of time. Research has shown that mild stretching is beneficial to tendon healing from a week after an injury.
The first step in fixing the patellar tendon pain is letting it rest a bit and using some ice. If you ice your patellar tendon do not overdo it, use it just for 15 minutes at a time. Ice gels like the TheraPearl knee wrap make this really easy.
For some people heat works better than cold - the only way is to find it out for yourself. Patella straps can help with the pain too.
Full rest is usually not required, just make sure you stop doing whatever causes the tendon pain. Do not take any anti-inflammatory drugs before speaking with a specialist - these drugs can either fasten or hinder the recovery.
The best exercises to fix your patellar tendon (and other tendon issues) are eccentric strengthening exercises. This simply means that you will have to do squatting and stretching on a slant board. Using a slant board is beneficial because it stretches your muscles. Once your muscles are a bit stretched, the constant pulling on your patellar tendon will stop, and the tendon will get ample time for regeneration. You can simply order a slant board here (suggested) or here if you do not have one yet. There are quite a few reasons while eccentric exercises are beneficial, from tendon length changes to tendon structure changes. While the reasons are not fully understood, eccentric exercises just work.
The two best exercises for patellar pain are slant board stretches and slant board squats (also known as decline squats).
To stretch your calves, stand on the slant board with your toes toward the higher end. First push your body up, then slowly, in about 10 seconds let your heels back on the ground. You can gently rock forward and backward too. Do this 5 minutes a day to stretch your calves. Do not force this exercise if you feel any pain. It's important to keep your legs straight while stretching, so that your calves do the work, and not another muscle group.
For slant board squats, stand on the slant board with your toes toward the lower end. Keep your knees close while slowly lowering your body until your thighs are level. Hold it a bit then slowly raise your body until your upright. Do three times 15 repetitions of this exercise in the morning and in the evening to fix your tendons.
To make this exercise even more effective, you can hold your hands level and your body tight while you are squatting. Breath in while lowering your body and breath out while raising your body. For maximum effectiveness pick a spot on the wall in front of you and keep this spot in focus. Do not look up or down.
Runners Connect has a short but effective article on patellar tendonitis. If you love lots of details, you'll surely like Martin Koban's take on the issue here. According to science eccentric exercises are very good for tendon problems. Why they work is still not yet understood. You can find some theories here. There are very helpful videos on youtube too, for example this one - just search for eccentric squats patellar tendonitis.