An at-bat is a chess match between the pitcher and the hitter. While some players like former MLB great Larry Walker claim that they simply swing at whatever pitch is thrown to them, most hitters should be figuring out what pitch they are going to see when they they're standing outside of the box, adjusting their batting gloves.
Everyone has a different approach to the first pitch. Some coaches insist that their players should never, under any circumstances swing at the first pitch they see, but others believe that it's the best pitch they'll see during an at-bat. Hitters should listen to their coaches, but if they haven't had any guidance, they should have the same approach as they would if the count was 3-0 and they have a green light. If it's a perfect pitch down the middle of the plate, swing away, but if it's close, let it go.
When the pitcher is ahead in the count (i.e. 0-1, 0-2, 1-2), it's rather unlikely that the batter is going to see something he can hit easily. Pitchers are known to experiment with their pitches in these situations, so hitters can look for breaking and offspeed pitches here.
It's much easier to figure out what's coming when the batter has the edge (i.e. 1-0, 2-0, 2-1, 3-1). In this case, the pitcher wants to throw strikes and is much less likely to take risks. Consider who's on base, too. If there's a runner on third, you can bet you're not going to see a curveball or a slider, but if no one's on, the pitcher may be more willing to surprise the batter.
When the count is full, hitters just need to make sure they aren't fooled. More often than not, they'll see a fastball, but it's definitely not unheard of for pitcher to sneak in a changeup or other offspeed pitch.