What committees and sub committees are involved in making a bill a law in the federal process?

Answer 1

any and all of them. A congressman writes a bill in Committee, or submits it to the floor where it is usually assigned to committee, unless there is a discharge petition to bring the bill to a vote. that requires a large number of members to sign.

The committee hammers out the bill into the best possible form.

Answer 2

Actually, under the current rules of procedure, a Bill is submitted to the Speaker of the House who can assign the Bill to one or more committees. There are a number of ways to discharge a Bill from Committee and move it to a vote.

See the detailed steps in the referenced source.