Each blockchain project has his own ICO participation protocol. I will show you one in this article.

Coinlist (I used my referral link :-)) is a platform where ICO are performed. You can freely create an account and wait for upcoming ICO.

Next ICO are available on the dashboard view : 

To participate you only have to send crypto on coinlist wallet or directly deposit on the platform using transfer. When your account is credited you have to register to the auction and complete a form with your bid with the unit price of the token and amount that you want (If you do not know how a dutch auction works go read this article : ICO Dutch Auction).

When the auction start you are able to follow it in real time on the platform :

At the end of the auction you will receive your coins according to the blockchain project condition.