It didn't. It made existing tactics more effective.

Keep in mind that the IJN shot to pieces the Russian Baltic Fleet at ranges exceeding the medium caliber guns that were on existing battleships. Dreadnought-type battleships simply deleted the "medium caliber" guns that were of marginal, at best, utility for more bigger caliber guns.

It wasn't a really revolutionary design, as in, no one had thought of it. Multiple people had put forth the idea of single-caliber large gunned battleships before hand. A Italian naval architect proposed such a beast before the Battle of Tsushima validated the "longer range + big guns > mixed caliber batteries", for instance. The USN began design and long lead work on the South Carolina-class before the RN started work on the Dreadnought. And you know what?

Battleship tactics didn't change. The major navies continued to attempt to employ dreadnoughts like major navies employed line ships a hundred years previously. When Oldendorf Crossed the T at the Surigao Strait, it would have been a tactic familar to naval officers of the Napoleonic era, except for the ranges involved.

All that said, naval warfare did change quite a bit during that era, but it wasn't nessecarily driven by battleship development. Aviation and submarines changed warfare more than "deleting mixed caliber battleships".

As /u/R_B_Kazenzakis says, it did not change naval warfare as much as it changed naval design. Even though others were designing or even building similar ships, the HMS Dreadnought was first in having a large standardised battery AND a very high speed.

What was revolutionising with the HMS dreadnought was that when it was put into the water, she was strong and fast enough to place herself at the ideal firing distance for her powerful main battery - and keep herself there due to her higher speed. Thus she could choose the time and situation she wanted to engage in.

When she was taken into service, she could probably have defeated 4 pre-dreadnoughts on her own.

So she revolutionised design (well, many had the idea, but the British were the first to implement it in a ship taken in service) rather than tactics.