how to go about leaving country on a long overstay? And possibly clear it?

SoIve overstayed my visa by over a year and plan on leaving in a couple days. 3 mains issues 1. the overstay 2. lost departure card 3. fresh passport with all clear pages (have old passport with most recent visa). How should I go about to ensure that if I get a plane ticket and turn myself in I wont end up being detained and missing my flight? Should I contact the american embassy regarding this? Also Ive heard its possible to avoid blacklisting through some sort of agent? Where can I find said agent?