If election is true, how are we
responsible for our actions?

Paul did not like this question, because it implies that God is not fair, so he responded this way: “Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus? Hath not the potter power over the clay, of the same lump to make one vessel unto honour, and another unto dishonour?” (Rom 9:20-21).

All men are responsible for their sins, and they will pay the price for them in the torments of hell for eternity, unless God elected them to enjoy the free benefits of Jesus Christ’s death for them. Those elect that God has saved from their just death in hell can only know they are God’s elect and assure their hearts and minds by bringing forth much fruit in the way of good works (I Thess 1:2-4; II Pet 1:5-11).

See Also

More detailed considerations about election: What if Election is True?