What will you see in terms of naval warfare? Almost no change whatsoever.
Rail guns are very impressive, but in the end, they only do two things: provide longer range within a smaller space. Why do I say this?
Because you can throw a rail gun slug a lot further (well... assuming modern tech...) than you can a chemically-motivated slug.
And the space needed to power a rail gun plus the ammunition for the rail gun is a lot smaller than the space required for the same kinetic impact in terms of shells and powder. (Granted, this assumes that you're using nuclear power. You're using something a whole lot more impressive than fuel oil to use rail guns, otherwise you won't have nearly as many rail guns in play and they won't have a significant impact on combat).
But you still have line of sight tracking. In other words, unless you allow for satellite tracking (invented in 1959, the naval Transit tracking system for tracking submarines) or some form of AWACS (invented in 1977), you're stuck with the fact that you can only "see" as far as your ship-based radar will allow you. And that limit is the horizon.
And the horizon is the key to success
A rail gun could certainly throw something beyond the horizon, but without the ability to aim it, you're just taking pot shots. That's the value of an airplane and the reason aircraft carriers became (and remained) the dominant naval craft. An airplane can fly beyond the horizon.
In short, other than sinking the Bismarck sooner or perhaps not evolving battleships at all... nothing will change.
Rail guns would make the faster cruisers and destroyers more valuable than the heavily laden battleships. This might be the only significant change — there would be little to no need for battleships as everything they did could be accomplished (and probably improved upon) by rail gun carrying and much cheaper to build cruisers and destroyers. Here's why:
Thanks to airplanes, by the end of WWII all battleships (world wide) had been retired or relegated to supporting roles. These roles were not insignificant.
Battleships were still quite deadly at night when planes couldn't fly.
Battleships were still used for coastal bombardment. Planes, especially bombers, could do a whale of a lot of damage and could reach further inland than battleships. But if what you want is a good old fashioned Baptist bible thumping, nothing could deliver the message more thoroughly than a battleship.
IMO, the faster rail-gun-enabled cruisers and destroyers would outmatch battleships for night maneuvers. I'm not entirely sold that they'd settle the argument as completely when it comes to a coastal bombardment (after all, dropping a 1+ ton shell bespeaks authority), but the ability to turn a little bit of that sand into glass on impact... yowzah.
But, all things being equal, would battleships really not exist?
And here's where I conclude that nothing would change. At the beginning of WWII the world (notably the U.S.) were building battleships — honking big boats carrying honking big guns. So, really, what would change? You'd still have navies building honking big ships with honking big rail guns and that would continue right up until the first patrol of planes from an aircraft carrier somewhere over the horizon sank the first slow-moving and very-expensive battleship. (Never underestimate the effects of economics.)
So, really, I don't believe a thing would change with one really minor exception: engagements would be a bit further apart.
NOTE: An early parenthetic deserves a highlight: rail guns need a whomping amount of power. I might be wrong, but I believe all ships today that use rail guns have nuclear reactors. You simply can't produce the power needed to use a rail gun with anything less unless there's just one rail gun on the ship and the vast majority of the ship's volume is given over to battery storage, meaning you have a substantial recharge time. This would mean rail guns are relatively rare and are good for basically only one or two shots ("Aaaaah! Rail gun! Shoot the rail gun! Shoot! Shoot! Shoot!"). Are you handwaving this? Nothing would really change either way, but striking a ship full of batteries that have partially charged would have a dramatic result ("No boom today. Boom tomorrow. There's always a boom tomorrow."). You'd find that supporting ships will not want to be anywhere near them.