All you need to do is copy the latest version of WSE (also make sure you have Warband 1.143 installed) into your warband installation folder.
Then run Brytenwalda by starting up warband through WSELoader.exe.
Now, anytime you start a fight, first click "Give me time to save". Save the game and click on the opponents again you want to battle.
Then, click "Setup Multiplayer battle", which will change into something like "Quit Game (won't save)". Click that, and you will be taken to the main menu. Press Multiplayer Game and click host game. Now you will be hosting the battle from the brytenwalda campaign, which other people should be able to join.
After the battle, click load game, and load your last save. Then click on the opponents you just battled, and select "Use multiplayer results".
I noticed there's still a few bugs with Brytenwalda and Battle Time though, plus a lot of the Brytenwalda-specific stuff (such as shield bash, tripping while walking backwards, extra backstab damage, ...) does not work yet. I also had some funny stuff happening to items, where their prefixes would disappear (a Chipped Warrior Axe turned into a Warrior Axe, for instance, and a Tempered Saxon Sword turned into a Saxon Sword after a fight). Hopefully this will be fixed
It's still loads of fun though to play with one or two friends.