Let’s start with the basics and get a bit more complex.
1. The enable/suspend groups button should always be visible. If the button looks like the image below, then groups are enabled. Otherwise they are suspended.
2. It’s a good idea to have shortcuts for enable/suspend groups, group, and ungroup. This is what I use:
option+G: enable/suspend groups
3. When groups are enabled, you move the group as one unit. When groups are suspended, you can move individual elements within the group while maintaining the existence of the group. Ungroup means the elements remain, but the group is gone.
4. If groups are enabled and you group 2 (or more) existing groups (lets call them A & B), the subgroups remain within the larger group (lets call this C). What that means is that if you ever upgroup the new group (C), groups (A) and (B) will remain. However if groups are suspended, all groups are suspended, not just the outer most group. This means to move group (A) in relation to group (B) you either have to ungroup group (C) or suspend groups and move the elements individually. It would be awesome to suspend group (C), but keep groups (A) and (B) enabled. But there are more important things in life. Note, if you make group (C) from groups (A) and (B) with groups suspended, the subgroups will be lost.
5. If groups are enabled and you move/rotate/copy/mirror a group, all the elements are effected, even ones on hidden layers. If some of elements are locked and groups are enabled, the entire group can still be moved, rotated, etc. If you have groups where not all the elements are visible at all times, make sure you know when groups are enabled/suspended (see point 1). Otherwise you will be angry and annoyed.
6. Groups can span multiple stories. You can’t group 3D objects in section/elevation, but you can group them in 3D. So if you group elements from the 3D window, you can have a group that contains a wall on the first story, a slab on the second story, a column on the third story, etc. If groups are enabled and you move part of the group on one story, the rest of the group on the other stories moves as well. In version 14 (maybe earlier versions as well), when you move/rotate/etc. the group in plan you will see the ghost of the grouped elements from the other stories as well.
7. If you group 2D and 3D elements in plan, then group multiple 2D/3D groups in the 3D window, you will be able to have 2D elements within the multi-story group. If you then suspend groups, delete all the 3D elements (in plan, section, elevation, or 3D window), and then enable groups again you will end up with a multi-story group containing only 2D elements. Try it.