How are the steps for a bill to become a law similar for state and federal law making?

At both the Federal and State level, a bill is introduced into the legislative branch.

From there, it will be put forth for discussions and hearings on the matter. It will likely be assigned to a sub-committee, who will investigate.

More discussion will occur and eventually the legislature will vote on it and send it to the Executive (Governor or President) who will sign it or veto it. The Legislative branch will enact then or will vote to overide the veto.

Depending on what happened, the bill will become law and the appropriate agency responsible will enact regulations based on the new law.