Slate has a helpful primer on how senators actually make it through 500+ amendments. The short answer is, they don’t, as most never actually make it to a vote.
My friend Keith Hennessey, while working on Senate Budget Resolution amendment marathons, came up with the term vote-a-rama for this process. In the vote-a-rama, senators serially vote on, withdraw, negotiate away, merge, or otherwise dispose of a seemingly unmanageable number of amendments. Although Keith may be a purist and say vote-a-rama can only apply to Budget Resolutions — and I expect to hear from him one way or the other on this — it seems an apt description of the process that will start up again on Tuesday.