The main opjective of Battle Tag is to find the star in a level and keep it for 2 minutes trying to avoid others from taking over your star.
Because a lot of people just don't know how to play Battle Tag, I give here a summary
The first thing you have to do in Battle Tag is to find the star. There is only one star in the game (if players don't lag to much) and it lies somewhere in the level. When you find the star you have to drive over it and you'll see that your car gets a green glow. This means you have the star and you'll see that your time in the upper-left corner will go from 2 minutes to zero. The goal is to keep the star (the green glow) for 2 minutes and avoid other drivers from taking over the star by tagging your car or passing close to it. When you don't have the star and someone else does, the red arrow on your screen shows you the direction where the car with the star is. When you are the first one to drive around with the star for 2 minutes you win.
The Tactics section tells you how to drive properly in order to reduce the chance of running into your opponents who are mostly ready to take over your star. The jump section will explain you how to jump properly.