If you look historically probably the most influential president at trying to move the economy was FDR and even his new deal was almost derailed by the US Supreme Court, e.g. minimum wage law, that was actually passed by Congress was illegal according to the court until the next year when it wasn't. Other presidents, Ford, Carter, even more pathetic.
So while the president can sometimes set the tone, either willingly or otherwise, outside of their appointment of the Chair of the Federal Reserve, not a lot they can do, assuming good will.
The president can influence what laws that congress at least proposes.
The president can regulate via the various government agencies (EPA - obama has used the EPA a lot, SEC, DEA, DOJ, HHS, OCC).
The president can put pressure on Congress to get certain law passed (he is not always successful, but always can start a public debate)