The youth center generates new young players for your team. These players might need some time to develop their skills before they become really useful though. If you increase the level of your youth center you will find that it can generate really good new players.
You need a training center at level 2 to build the youth center.
You can find out how many new players are generated each season. The higher the level of your youth center, the fewer players are generated. These players will be more useful to you though. The new players will be generated at random times during fixed intervals. If you get 7 new players per season (52 days) you will get one new player every 52/7=7.4 days. This new player will appear at a random time within these 7.4 days. This means you could get two one after another and then not get any for 2 weeks.
You can control the type of new players that are generated using the "settings" tab in the youth center. The higher the level of your youth center, the more options become available, giving you more control over the type of youths you'll be shown.
After a new player enters the youth center you can see it's statistics. While it is in the youth center it will receive training based on the level of your youth center. A level 4 youth center will train your youth players as well as a level 4 training center would. Players in the youth center won't be able to play matches though, so for their development it's important to move them to your real squad and select them for matches.
If you offer them a contract you'll pay a weekly wage. They'll then be moved to your reserves squad. From now on they are out of the care of the youth center and will receive training from your training center. If you want to use them for competitive matches you'll have to move them to your main squad.
There is a chance of 1 in 25 that your youth center will generate a supertalent. This player will have a higher talent than the maximum for the current level of your youth center. The other fixed skills of such player will generally also be above average.
To keep this a little more fair you are guaranteed to get a supertalent if your last 30 youth players were all normal players. Also, if you already got 2 supertalents among the last 25 players your next players will be normal youths. There is a "youth log" tab in the youth center where you can see your last 30 youths. Supertalents are marked with a star in this overview.
The extra players you receive when upgrading your youth center will never be supertalents.
Once you reach YC10 you can upgrade it to Youth Academy 1. The Youth Academy is a normal upgrade to the Youth Center. The exception is that starting from this level you no longer get 2 free youth players for each upgrade. It is also a lot more expensive than the lower levels so make sure you can afford it!