That vast expanse is all yours - the entire area beyond the dirt cutout for the infield. Now, you may have started in baseball thinking the outfield is where they put the players who can't make the infield. But as you grow in baseball you soon discover it takes something special to make a good outfielder - most of all anticipation and concentration. After all, it can get lonely out there - so you have to keep your mind on the game from the baserunners to the batters.
And never ignore the game inside the cut. First, because you may play other positions as well. But also because a good outfielder is always ready to back up the action on the infield - from simple throws back to the pitcher, to all-in rundowns.
Besides, you're the player with the leg speed, arm strength, and the desire to go all out. Need proof - check the plays of the day on your local TV station. It's always those great outfield catches they show. Be ready.
Essential Skills
Several pages for outfielders include motion-enhanced content. These animations of players in action are based on motion-capture data from one of the facilities which also provides this for video games - it's recorded from the real movements of real players in real time.
All drills help. Put extra effort into those targeted to outfield fielding & throwing. The drop down list here includes all team drills because you may be called on at any time to fill another position.
More for Beyond the Cut
Links listed here include special articles and features that will add to your knowlege of outfield play and what's expected of you.
Additional tips from the question & answer archive, for fielders in general and specifically for outfielders.