This curing soap instruction for cold process soap is what I've done at my soap store. It is better to leave your soap slab in the mold for a longer time than a shorter, too soft, time.
Basically, the curing has started the moment you poured your liquid soap base into the mold. The temperature drops to room temperature, the chemistry of the lye, water and oils continue to make a solid cleansing product, and the harshness or high ph of the soap is starting to decrease until it is a ph friendly bar.
After your soap has been in the mold for a day or two, take a look and see if looks and feels solid enough to remove. If you can gently push a dent into it, it is not ready. Give it another day or two. If you still aren't sure, loosen the soap with it's lining attached, from the mold. If you can pick up the lining from one end and the slab of soap stays solid and doesn't bend in the middle, it is ready.
If you've started to remove the soap slab and now it seems too soft, you can leave it as is for another day or two. It is the exposure to the air that will help it cure faster than if it were still sitting in the mold.
If it is ready, remove the lining carefully, and now you can start cutting the slab into bars. If the size of the bars doesn't matter too much, you can free hand the cutting. If you are planning on selling your bars, you may wish to buy a soap cutter to make the bars more uniform in size.
Place your cut bars on trays. I used to use cardboard trays (soda pop and beer flats) and could get about 24 bars on each one. Leave some room for the air to circulate around each bar, place out of direct sunlight, even better if you have a cool room, and leave for a week or two. After a couple of weeks, you may wish to turn the bars upside-down to allow the bottom portion access to the air. Leave for another two weeks.
The longer your bars can cure, the harder they will be, and the longer they will last in the shower.

This curing soap instruction for cold process soap is more of a safety issue.
A couple of precautions to check for when removing your slab from the mold, are to see if there is a layer of water-like material on the top. This is not just water, this is highly caustic lye water that has become separated from the soap base. To test this, you can place of drop of ph tester/phenolphthalein on the top to see how fast the drops changes color. If it is a layer of caustic water, try to get it to the sink without spilling any and rinse it off. You will probably need gloves for this. I have had to do this a couple of times, and the rest of the slab was fine.
Another curing soap instruction for cold process soap is to look for a layer of lighter colored, or white, soap base along the bottom of your soap slab. This too is highly caustic, and usually happens from a lack of stirring, which means the soap wasn't quite traced yet. Also, if you see little puddles of water in this layer, this is caustic lye-water.
In my early years of making soap, I would still get the occasional bar do something like this, and I could not always figure where I went wrong. If this does happen, cut off the caustic part and discard, and place the rest of the slab on a tray to cure. Give this perhaps-damaged slab a week or two to cure, then test it with the ph tester. If it tests low for ph, it is probably safe to use.
Your bars will actually loose some weight when curing as well. We were aiming for 4 ounce bars, cut them at 4 ounces, yet after they fully cured, they had lost 1 ounce of moisture. The usual weight loss from moisture is 1/2 ounce.
From the 'curing soap instruction for cold process' page, to more info about trace here.
Soap molds, what can use use for a mold, more here.