The Layer Manager dialog box will now appear as shown below.

First of all, make sure Use Groups is enabled by ticking 'Use Groups' as highlighted in Blue below.

Now select the Layer(s) you would like to Add or Move to a Group and click the Edit Selected button as shown below.

The following box will now appear.

In the Group section, select a Group from the list to move your Layer to, or just type in a Group name if you want to add a new Group, then click OK.

You will now see that your Layer has moved to the Group (see 2nd image below).