The users could be, for example, based solely on a percentage of your overall user base (10%). The rollout should be customizable (configurable) and support any number of features. It would also be useful to associate rollouts to specific user roles or privileges (ACL).
So, in essence, what is an architecture that would scale reasonably well?
As for the language agnostic portion, you can either provide pseudo-code, general concepts or ideas, or snippets from your preferred language to get your point across.
Links to any examples or tutorials are welcome.
My recommendation would be that, for the people who are getting the new feature, the site they are on should be as close as possible to the site that everyone will be on once the feature is public.
In other words, I wouldn't have, for example, conditional logic on a page to determine whether a button should be visible or not, if that condition would only exist during this beta period. Rather, I would determine at login time whether this person is a beta participant or not (that determination might be random, might reference their role, etc). If they are a participant, they would be redirected to a separately deployed site that is deployed from a version control branch.
Once the rollout is complete, the branch is merged in and everyone sees the new feature.
This way, you don't have to worry that the codebase the public beta users are seeing is different (in some way that could break something) from the eventual release codebase.