Battles are turn based affairs where knowing how different types of moves affect different type opponents is all important. For example, the water type move, Surf, is super-effective against a ground type foe but not an electric type. Your Pokémon gain experience by winning battles. The experience allows them to level up and leveling up allows them to learn new moves and evolve into new species. You can add more Pokepals to your party by fighting wild Pokémon and then catching them in Pokeballs.
So, the basics have not changed but there are a few new elements to game mechanics. Double battles had been introduced in previous iterations but Pokémon White introduces triple battles. Three Pokémon from each party are on the field at once. In a triple battle a Pokémon can only attack an opponent one away from it. So your Pokémon that is farthest left cannot attack your opponent's that is farthest right. This adds a new element of strategy to the battles as you now have to worry about not only type matchups but also placement of types. There are a few other gameplay changes as well, but delving into them too deeply would spoil the experience for those playing.
The game is not as punishingly hard as older versions. HM moves (Hidden Machines are special battle moves that can have effect outside of battle) such as Strength and Cut can still be acquired but are no longer necessary to continue advancing the quest. In previous games you would have to have attained Cut to cut down a bush that was in your path or have to have acquired Strength to push a boulder out of your way to advance to the next town. The gym leaders still have preferred types, but you will not find yourself stuck against a gym leader whom you cannot beat because you have not yet caught the right type of Pokémon to do so.
There are three different ways to connect to Multiplayer – wireless, the Nintendo Wi-Fi Connection, and IR. Wireless uses the DS wireless signal to create a link between your DS and another in close proximity. Connecting to the Nintendo Wi-Fi connection is simply connecting to Nintendo’s worldwide server using your DS’s internet connection. IR stands for Infrared and by putting your DS back-to-back with friend's DS you can quickly launch a battle or trade. The lag over IR is much less than the lag using wireless connection. If you are interacting with a friend in the same room, IR is the preferred way to interface.