If he and his friends can keep talking, they can keep going until cloture is invoked. That takes a couple of days and 60 senators. See http://en.wikipedia.org/wiki/Cloture#Procedure for the exact procedure.
That's the idea. So long as he has the floor, they can't vote. But he can only keep the floor so long as he keeps talking.
Can he realistically achieve anything here?
One person can't usually achieve more than a political statement, because one person can't usually talk for long enough to have a meaningful impact. Successful filibusters usually involve the cooperation of a number of people.
> How does this work, only if he stops can the process continue?
The senate isn't actually discussing or voting on the USA Freedom Act today (floor schedule is for discussions of an unrelated trade bill) and this discussion can be cut off tomorrow anyway, so this isn't technically a filibuster (yet).
There's a provision in the TPP (which is this 'unrelated trade bill' you speak of) that allows for extension of 215 of the USA PATRIOT Act. It's not a filibuster; but it's definitely related to the TPP.
Wait, what, really? This is my number 1 thing about Congress that grinds my gears. Attach little bits of (significant) legislation, many times at the last minute, that have absolutely no relation to the bill's topic. At least this time Wyden and Rand Paul are doing something about it.
Sadly, this happens all the time. And it does it in really sneaky ways, things like "Strike paragraph 1a from USC 1234 that says 'June 30, 2015' and replace with 'June 30, 2019'". That way if you're searching through the bill, you not only need to know what those other bills are, but those specific paragraphs are; and there's no way from just reading a bill what the intent is.
Just as newspapers, radio and television, etc. have brought increased transparency and clarity to the inner-workings of government, likewise we should definitely be using even more recently developed tools like branching, revision histories, hyperlinks and various diffing algorithms to elucidate exactly what has been or is being proposed or adopted and by whom.
It should be a point of procedure that all bills do exactly one thing. Small and easily reviewable commits, please; software engineers learned this long ago.
Page-by-page of a single bill doesn't work, though; see also attempts at a "line-item veto". For the most obvious failure mode, consider a bill that replaces one tax with another and a veto on the removal of the old tax. Or consider a bill that adds a tax and a service funded by that tax, and a veto on the service but not the tax.