How did Moses carry on God's plan?

Not sure exactly what you mean by "carry on gods plan", but here's an answer to what I think you mean.

Moses was able to go to Egypt, confront Pharoh, lead the people of Israel out of Egypt and lead them to the border of Canaan because God wanted it all to happen and worked miracles to make it happen.

In The Bible, in the book of Exodus, Chapter 3, verse 8, God tells Moses His plan:

"I am coming down to deliver [Israel] out of the hand of the Egyptians, and to bring them up out of that land into a good and large land, into a land flowing with milk and honey".

Moses was able to lead, because God promised that He would lead Moses and help him. In Exodus chapter 3, verse 12, God says to Moses "I will be with you" to assure Moses that he'll be able to do all that God commanded him.