I'm emphasizing "Current" and "for Beta" because I think this is probably going to be subject to change.
In Legion, you'll have access to all three of your specs, changeable at I believe any time you can currently switch between dual-specs.
However, the Beta patch notes now inform us that this will incur a gold-cost, and this will be a progressive gold cost, which actually used to be the case back in Vanilla through I want to say Wrath when changing your specs (of course Wrath introduced dual-specs, which used to be 1000 gold - and that used to actually be a large amount of gold, but it would then negate all further expenditures on re-speccing unless you wanted that third spec.)
While I'm polishing my pitchfork tentatively, there is one aspect to this that could make things far less worrisome than they might be, namely that if you enter a dungeon or raid using LFD or LFR (not sure about queueing for PvP) as a tank or healer, it will automatically switch your spec for free as you enter and leave the instance.
This actually covers 95% of the times I'd be switching specs, as I tend to solo as Retribution and do dungeons almost exclusively as Protection.
There are definitely some potential problems with this system. For instance, if a Priest who is soloing out in the world as Shadow decided to heal a dungeon, which spec does the game choose for them? And what if you like to run, say, Frost while soloing and switch to Arcane for group content? What about world bosses? What about if you're tanking in a group quest but you want to go DPS for a dungeon?
Like I said, I'm definitely sharpening my pitchfork and gathering torches, but I'm not ready to get out into the streets just yet. This is Beta, after all, and even if it's a far more complete and polished Beta than we've had in the past, it's still very much subject to change.