Rest , NSAID. Although there are many recommendatins to treat elbow tendonitis i feel the most important is resting from the aggravating activity. Generally the inflammation from tendonitis is caused from overuse. General recommendations for initial management include rest, ice , antiinflammatory medications such as Ibuprofen or naprosyn (naproxen). Your provider may also recommend a splint for immobilization.
Stretching. Probably the most useful modality for treating the elbow tendinosis besides rest is stretching. Stretching before activities that involve the hand and wrist will keep the muscle attachment from the stress of the activity. Stretching every morning will also keep the elbow from starting the stress to begin with. The stretching can be supervised by occupational therapists or done at home.