What to do for homecare nursing for someone with deep vein thrombosis?

Depends. Activity should not be restricted. Bedrest is actually not recommended any more. Rather frequent blood tests are needed, initially, as dr. Toppin mentioned and once or twice daily shots are often given for a few days. It is important to watch what you eat on some blood thinners. But for someone who has been, otherwise, relatively healthy, there might be little need for homecare nursing.
Family conference. Meeting with the patient and their md is vital. During that visit the medications, and activities will be discussed. The most important therapy will be the medication to make sure another clot does not form. The patient will usually need weekly blood tests until the levels are stable. Emotional support is also needed in order to aid their return to good health.
Dvt. Making sure the persons taking the necessary anticoagulation medication. Maintaining an active lifestyle, simply walking around. Making a home safe from falls or any type of trauma which may be exacerbated with bleeding secondary to being on anticoagulation therapy.