The saponification reaction will go through several phases:
Trace - thick like pudding
The soap will continue to harden from this point
The speed of the hardening will depend on oils/heat/certain FOs or acidic additives which will act as a catalyst and accelerate this process.
Once the soap is very very hard it will continue to heat up unless you do something to stop it (freezer, outside, fans, etc)
At this point the soap will gel - look like vaseline
After about an hour at this temp (195 deg F) the saponification reaction is complete and the mixture will start to cool
The soap will become hard once again
If your soap seizes (reaches the very very hard stage) - all is not lost. Just heat the soap gently in your pot on the stove - give it a stir when you can and the soap will gel. You can now glop it into your mold
Sometimes the soap will OVERHEAT when it becomes very hard. Acids will cause this to happen (milk esp). The whole thing will fall apart into soap curds floating in oil. Again, all is not lost. Heat and stir stir stir and you will get gelled soap once again. Once you have gel your soap is complete and there will be no more surprises (the reaction will not spontaneously run in reverse)
Hope this helps!