I'm going to share what NOT to do -- assuming you are a company like ours. I am in the IT department and we have about 15 techs, 10 of which are "front line" Help deskers as we call ourselves.

We answer the phones and field emails for our 5,000+ healthcare professionals (internal employees). Some of us have strengths in various areas but we all are trained to do almost everything.

I made two mistakes with groups:

I created too many groups. If you are like us, you probably don't need 7 groups for 15 people. It makes assigning tickets to agents more time-consuming than necessary.

This sounds like a small thing but since everyone was in about 5 groups, there was also a lot of overlap in the group membership and it was very confusing. I'd recommend having your agents in a maximum of two groups, and only in one if at all possible. That way, when you type their name to assign a ticket to them, they only show up once in the drop down list.
I created a group that became a bottleneck to expediency. We called it the Triage group and the idea was that all new tickets would automatically (via a trigger) get assigned to this group. And then two agents were supposed to monitor that group (via a view showing only those tickets). They were supposed to be the gatekeepers. They were to assign the tickets out to the other Helpdeskers and also email back to the requesters to get more info if they had forgotten to include something that was necessary for us to solve their issue.

The problem was that those two gatekeepers got busy and became a bottleneck so that I had to allow access to the Triage group to everyone and then it became meaningless. In fact, the problem got compounded because I had set up a trigger that would re-open any ticket that was solved in the Triage group because I thought I would be running reports on groups and Triage was not what I considered a "real" group.

I suppose if you have a larger organization and can devote 2 people to the task of triaging your tickets and passing them on to the other agents this might work but for us it was a major failure.

The interesting thing is that our agents got used to this inefficiency and have made our Zendesk work in spite of my ill-conceived plan. Anyway, I just spent 2 hours fixing all of this - triggers and groups and views and automations. What a nightmare. I hope my pain and experience will save you some of the same.

I'll let you know if our new system works better. Fingers and toes crossed.