How to make youth clinic/camp fun?

Based on your post I would assume this is a high school offering a camp for youth players?

It depends what the goal is.  It also depends what the cost is.  

Keep them busy in an organized way.  Standing around equals boredom.  I have seen camps with groups of kids broken up into different groups working in groups of 4 or 5 at each "station" and getting plenty of reps.  I have seen camps with 70 kids and two instructors.  So, few reps and lots of standing around.  Try to get the kids plenty of reps.

The young ones probably won't get a ton of verbal cueing, have the high school kids show them what you mean or what you are trying to teach. 

Doing some little contests built into the drills can be fun....sprint time, throwing to a target off of the mound and tracking it.  Just little prizes, nothing that would cause jealousy.  If you are having a break for a snack or lunch have the high school kids eat with the campers.  At the end of the day a young kid looks up to a high school kid in his high school baseball uniform.  A 10 year old can see a 16 year old who can throw the ball 80 yards like he is a hero.  My son went to several youth camps when he was young, usually had fun.  It was a youth camp so it was not super intense and instruction was ok.  What he would talk about most on the way home was the high school players and what they could do.  

The things my son talked about after attending youth camps:

1. If he stood around I never heard the end of it, but as long as he got moved from station to station or had a lot of reps he had fun.

2. Hit the "_______", he had two favorites. Place a trash can at first base and have the rest of the infield field the ball and hit the trashcan. They LOVED the loud thuds.  His other favorite was a bucket placed on home plate.  The throw from the outfield had to hit the bucket in some way...this one rarely happened, but it gave them a good place to aim so he liked it.

3. For the pitching part of the camp the coaches put up several hula hoops onto the fence, marked off the appropriate distance for the mound, and had a competition of how many kids got strikes by getting it in "the strike zone". 

4. Aim your bunt, the coaches laid out paths with other bats on the ground and the bunt had to be laid in a very specific spot (at least 3 foot wide) or you had to run the bases.

And the number one thing I heard him talk about when attending a camp..."Did you see how FAST those older kids threw, will I throw that fast one day, did you see left field playing catch with right field, unbelievable!!!!!"

Teaching sliding on a slip and slide on the last day! They will talk about it for a year.