I understand that this may be very similar to that used by the Union, the same possibly, but I would wish for this to be clarified to me. An example of my own country's process (NZ) is, first, there must be a public submission, for some sort of legislation, then if it is randomly selected for discussion it becomes a bill, and is discussed and debated by the Select Committee. After those happenings it is juggled between the S. C. and the Parliament for refining purposes until it eventuates into a law after a successful vote.
Example: A Confederate senator would propose a bill before the Senate. At the most basic level the bill would go before the full body for a vote. If it passed, a Representative would propose the same bill before the House. If it passed, it would go to the Confederate president (Jefferson Davis from 1861-1865) for his signature. He could sign it into law or veto it. If he vetoed it, the House and Senate could vote on the same bill again. If they achieved a 2/3rds majority, the bill would become law regardless of the president's veto.
This is detailed below in the Confederate Constitution, which is almost the same as the American Constitution, except that the Confederate president had the use of a line-item veto. This means he could veto part of a bill but sign the rest into law.
"(2) Every bill which shall have passed both Houses, shall, before it becomes a law, be presented to the President of the Confederate States; if he approve, he shall sign it; but if not, he shall return it, with his objections, to that House in which it shall have originated, who shall enter the objections at large on their journal, and proceed to reconsider it. If, after such reconsideration, two-thirds of that House shall agree to pass the bill, it shall be sent, together with the objections, to the other House, by which it shall likewise be reconsidered, and if approved by two-thirds of that House, it shall become a law. But in all such cases, the votes of both Houses shall be determined by yeas and nays, and the names of the persons voting for and against the bill shall be entered on the journal of each House respective}y. If any bill shall not be returned by the President within ten days (Sundays excepted) after it shall have been presented to him, the same shall be a law, in like manner as if he had signed it, unless the Congress, by their adjournment, prevent its return; in which case it shall not be a law. The President may approve any appropriation and disapprove any other appropriation in the same bill. In such case he shall, in signing the bill, designate the appropriations disapproved; and shall return a copy of such appropriations, with his objections, to the House in which the bill shall have originated; and the same proceedings shall then be had as in case of other bills disapproved by the President."