What will help to relieve trembling hands? Are they result of taking depression meds?

Tremors. Tremors are possible with antidepressants or mood stabilizers, and tx is by adjusting dose or adding beta-blockers such as propranolol. Consult your doctor.
Medication effects. You don't say what medications you are taking, but some medications such as tricyclic antidepressants and lithium can certainly cause hand tremors. You can also see this with ssri's such as Prozac (fluoxetine) -- 3-13% of people, supposedly. Talk with your psychiatrist about this, and see what can be done to help.