To those that have contracts, how do you get the contracts and how do you manage them?
Contracts
For getting them, a minimum of 50k words and 200 collections, plus a stable release date is needed. When these conditions are achieved, you can either contact a content editor on discord and ask for a contract or the Content editors/webnovel will reach you first with an email or notification.
For managing them, that I honestly don't know
Hi. Okay, to be honest, the best and fastest way to get a contract is to join the upcoming WPC. If you have enough courage to join then you can.
But make sure that you will abide by the writing contest rules for you to have the bigger chance to win.
Also, updating daily is one of the best ways to catch the reader's attention.
Anyway, keep writing, win or loss 
I wait for an email or a notification in Inkstone. Please specify what you mean by manage them. Once you sign the contract, that's it. You just continue writing the story. To ensure I get the minimum guaranteed sum, I make sure I write at least 1,500 words and upload a chapter everyday, best is to schedule them at regular intervals.