I am running a campaign, I have the Master tier subscription.

I found a Magic Item that someone homebrewed and added it to my Homebrew Collection. When my player goes to add this to their character sheet, do they simply search for the item as normal and add it, since it is in my collection? Or do they need to go out there and find it, add it to their collection, and then add it to their sheet?

Everything in everybody’s “collection” is automatically shared with everyone they are in a campaign with. So not only is everything in your collection automatically shared with them, everything in their collections is also automatically shared with each other and with you too. You don’t need Content Sharing for it to happen, and no subscription is required. Well, not for the sharing part anyway, you only need a subscription to add other people’s homebrews to your collection.

So this isn't working right for me and I want to clarify if this should work.

(1) I am a player in another person's campaign.
(2) I put some monsters in my homebrew collection
(3) They don't see them

They don't have a subscription (but I am the top tier), is that the reason?  Something else?  Or should it work?

They would only be able to “see them” under the Extras section of their character sheets unless you send them the URLs for toes monsters.