There are two main reasons for building a starter and two main ways to pitch it into your beer, what works best for you and your procedures is up to you to decide.
If you make a starter and pitch quickly (within about 24h) what you are really doing is trying to enhance the health and viability of the yeast cells. Many people make a starter at the start of their brew day and then pitch it into their beer later that day, that way they are ensuring the yeast is active and healthy when they pitch it.
The other main reason for building a starter is to increase the yeast cell count, which means you need to give the yeast time to acclimatize, reproduce and start fermenting. For most yeast you'd need to wait 18-24h to be sure they have finished most of their reproduction.
Some people pitch the entire starter volume, since it's easy and quick, however this works best when your starter wort is very similar to your beer wort, else you might end up with off flavours other issues due to the differences in wort.
Other people prefer to let the starter fully ferment, and then cold-crash it in the fridge (usually 1-2 days to ferment and 12-24h in the fridge), that way they can decant and discard the spent starter-beer and pitch only the yeast. This is also useful (as mentioned in How to Brew) to help the yeast build up their reserves so that when they are pitched into your wort (especially if the wort is different to that of the starter) they are in a good condition to adapt and are ready to reproduce and ferment your beer.