Hi C.!
Sound like you have a fairly typical (or at least not uncommon) 18 month old. Let me ask you a few questions to think about. Is he a first child? Does he speak fairly clearly yet? What sets off the temper since he is fairly laid back? At this age a lot of behavior can be due to frustration. They might not be able to communicate well, they may have in mind how something should work and they can't make it happen, if it's related to sharing have you ever heard of the Toddler's Creed?(if not, let me know, i'll find a copy.)
Acknowledge his anger. Say something like "I see you're angry" or "That makes you frustrated when it doesn't work" This teaches him the words for what is going on. Then show him what to do with those feelings or a way to solve the problem.
If his difficulty is communication, help him find ways to do that. If he's not talking yet basic signs can help (it doesn't have to be formal sign language, anything simple and meaningful to the two of you can help.) Give him an acceptable way to show anger (for now, could be squeezing a soft ball really hard, briefly making a loud noise, or whatever you find appropriate.
If he's frustrated because of his abilities break it down to simple steps he can do or do it with him (your hands over his).
In the heat of the moment, some techniques that may be helpful are: distraction and redirection to a new activity, remove him from the situation, if he's not hurting anyone ignoring the behavior sometimes works.
He may need a break from playgroup for awhile (unless this is your chance to connect with others) or less often (if its daily) or just make sure the toys are soft!
I think the real key is to figure out what sets the tantrum off and address that issue.
Biggest thing: Don't stress yourself out over this at this age. A lot of this goes away as they grow older and learn other ways to express anger.
I hope this is helpful for you.