Yes, a Form 8332 should be filed and attached for each child.
Keep a copy for your records and for future years. You can elect to release the claim in future years by filling out Part II of the form. Otherwise, you'll have to get the non-custodial parent fill out forms for each child every year.
You don't need to fill out anything else, but you need to mail your 8332s within 3 days of e-filing to:
Attn: Shipping and Receiving 0254
Receipt and Control Branch
If you're paper filing a 1040, find your state here.
If you're paper filing a state return, find your state here:
