It depends on what latex you use. I use monster maker's mask latex and usually have no issues.
First, the mould should be plaster, so it can absorb some of the moisture from the latex. That makes the latex touching the plaster set thicker and less runny.
Don't fill the mould and expect the whole lot to dry to form a solid object. Liquid latex is for making a hollow skin.
You fill the mould, let it stand for a while (20 minutes, half an hour, an hour, it varies), then pour it out of the mould back into your container. Some latex will be left on the surface of the mould. Leave it to dry. This may take a few hours. The white latex will go semi-clear, with a yellow-brownish colour.
When it is dry, dust the inside with talcum powder, this is to stop the latex sticking to itself as you peel it out of the mould.
You end up with a hollow latex skin. The longer you left it to stand, the thicker the skin will be.
If your mould is a non-absorbent material like fibreglass resin or silicone, it dries better if it is a big open mould so it is exposed to plenty of air. You have to paint on a thin layer, let it dry, and then paint on another thin layer and let it dry, and repeat.
Some heat and moving air will help to dry the latex, but you aren't trying to bake it like you would with foam latex.
Here is a simple object - a shoe - being cast in liquid latex: https://www.youtube.com/watch?v=BfwIgSC9Ka8
Do not use the liquid latex that comes as part of a kit for making foam latex. That is because it is not vulcanised,and will not set like the stuff that is sold as 'liquid latex'. This is also called pre-vulcanised latex, and is used like Nick says above.