It's a frustrating sport, in that there are a lot of whistles and play stoppage. But, that generally gives me time to set up for a shot, especially a 'free hit'. These are usually great since you can isolate on the shooter, typically a middie or defender.
I tend to stalk the sideline up about 10-15 yards up from the endline. If there's a 'corner', then I get behind the goal, about where the circle will intersect the baseline and watch how they play it, do they shoot it out to a player who shoots, or passes it to someone else?
Penalty shots are rare, but offer a great opportunity, they're about 7 yards out from the goal.
What surface are you shooting on? What age level? Do they wear face masks?
Here's a post of a game I shot last week, I *think* you can see them w/out being a member.
I move up and down the sidelines. Sometimes I wait for the play to come to me. Sometimes I try to follow the play, especially if it looks like there may be a corner. Beware that in some places you are not allowed behind the goal line. If that is the case I try to position myself aligned with the player I think will be the shooter and on the sideline that will give me a shot of the face. Sometimes I will shoot from as close to the goal line as I can (without going behind it) but many times the players running out from the goal block my line of sight to the shooter.
As much as my knees can take it, I try to shot as low as I can. I feel shooting lower gives me a better chance of catching the eyes of the players. Field hockey is very frustrating that way as the players are almost always looking down.
Of having the lens reach in a big help. 300mm, 300mm +1.4 TC. 70-200mm works but you have to be more patient waiting for the play to come to you.
If you are focusing on one particular team, (sunlight allowing) pick the sideline that will give the most access to the players faces (almost all players are right handed).
I like to sit at the end, halfway between the sideline and the goal. 400 and 70-200.
I always sit to the right of the goal if you're facing midfield. Has never failed me.
I have been shooting field hockey for 6 years now...HS and now D1 college but I shoot from the sidelines since I do not have a field pass...here is my gallery from this years shots...I use the 300f4 with a 1.5 mostly, last game pulled out the Sigma 120-300 with the 1/5 tele...