To create a service group, you're first going to go to Setup > Services and click on the button at the top to "Manage Service Groups":
In this example, I have a number of different tutoring subjects and I want to sort them into groups so that from my tutoring website, students who are interested in getting tutored for, say, math can go to the "Math Tutoring" page on my website and only have to choose from Math subjects instead of all the subjects we offer tutoring in.
From my "Add & Manage Service Groups" page, I'll first click the button to "Add New Service group":
Next, I will name my service group so that it is easily identified:
Then, from my list of services, I will select all of the services that I want to display on the scheduler for Math Tutoring options and then press the "Next" button at the bottom:
After clicking "Next" the service group is successfully created and you'll be taken back to your main "Service Groups" list screen. You'll see the service group you just created, the services that are in it, and the unique URL that it is available at:
If you click on the service group, you'll enter into the service group's edit screen and you can click on the Private URL for that service group to check out the scheduling flow for it:
You'll see by clicking through that private URL that on the "Services" screen, only the services in the service group show up.
If you would like to show your newly created service group in your company scheduler go to Setup Tab > Service Group Panel and check the box next to Show Service Group: