On Monday, February 4, 1861, delegates from six of the seven states that had seceded -- Texas delegates would be along later -- met in convention in Montgomery, Alabama. They worked mostly behind closed doors to form over the next few days to form a new government and elect the officials for the Confederate States of America.
They worked quickly. It was important to them to have a functioning government up and running before Abraham Lincoln was sworn in as president on March 4. They also wanted to be up and running so that cooler heads could take over the situation at Charleston. South Carolina Governor Francis Pickens and some of the other secessionists might start a war before any preparations could be made.
The delegates would adopt a constitution, elect a president and vice president, and appoint themselves the new Confederate Congress. It was all provisional. The constitution would still have to be ratified by the states and none of it would become more permanent until February 1862.
After that first hectic week, they would settle down to complete the formation of the new government at a more leisurely pace. At one point, they simply decided that all U.S. laws except those that conflicted with their new constitution would remain in effect in the Confederate States.