This is a search for hidden talent. Know what you're looking for. But remember - even MLB scouts don't always pick winners!

Pick priorities.
What is it you need most? First find pitchers, then power hitters, catcher, middle infield, etc (Your personal order may be different, but have one!)

Move past obvious.
If a player has one obvious talent you really need (home run power, great glove, whatever) then stop looking at him for the rest of the day - you know he's a pick.

Set targets.
The more specific your need, the more focused you'll be. Check WebBall's Player Norms page for some possible target numbers.

Player Rankings
You must have a scoring/ranking chart. If the co-ordinator only provides a roster list, make your own chart.

Think ahead.
Always scout with the Draft in mind. Could you possibly get every pick you want? How many alternates (utility players) will you need to scout for? Once you have identified your 'star' core, your team will really be built on the quality of your play-anywhere, put-me-in-coach players.

Eliminate early.
Part of the exercise is also deciding who not to look at. Don't waste time with drills that don't have an elimination factor. So, for instance, in the Round the Bags drill, in a normal practice you would keep everybody in, at a tryout one miss (or two) and a player is pulled to the sidelines. (If you don't want that kid to feel bad, have someone available to work with him on that skill, but you keep your focus on the best.)