Not only is it very doable but the US consulate in your new country will literally help you fill out the paperwork. 1. Move to a new country 2. Present proof

Not only is it very doable but the US consulate in your new country will literally help you fill out the paperwork. 1. Move to a new country 2. Present proof you have a new citizenship (you can't generally be "nationless" by international law or you end up remaining a citizen of whatever country you were last a citizen of) 3. Fill out the paperwork and pay $450. The consulate will assist you if you need help. If you can follow the instructions to bake a cake, you can surrender your US citizenship. It's neither difficult nor expensive.