Take a look at the end to end demo of sub requests and the administrative functions available.
When you're logged in as league administrator, you can click on Request Sub -> Add a Sub Reservation. From there, you can choose the round, the regular player, and the sub who is going to play for that regular player.
Alternatively, a player can make a sub request, at which time the subs will be e-mailed an invitation. The first sub to accept the sub request through the link in the inviation will "reserve" the sub request. You can control who gets notified of the sub requests in your League Settings in the "E-mail" setting's category. For example, if you're a two player team league, you can have the teammate be copied on all sub e-mail requests and confirmations.