How can you treat tendonitis in the archilles heel?

Several ways. Refrain from the activity that caused it, take pressure of the achilles. Usually this is shoe that has a higher heel (not real high heels). Then we do some deep tissue massage to improve blood flow. Then some gentle stretching. When the tendon pain calms down some more aggressive stretching and then some more challenging exercises to get the person back to usual activities. Nsaids can help too.
Some things may help. For inflammation at achilles' tendon near the heel bone, one can take Motrin 3 times a day for a few days to decrease inflammation. Decrease sports activities, and use a cold pack on the area 3 times a day after activities. Use a good arch support + shock-absorbing heel cushion, to avoid pronation from flat feet. Do gentle calf stretches. If not better, see an orthopedic or sports medicine doctor.