Groups can be accessed from:
The group button that looks like 2 persons on the bottom right corner of you screen
The > button in My groups on the Home screen
At the top are 2 tabs:
My groups - these are all the groups you have joined
All groups - these are all the groups in the same community
To access a group, just tap on the name of the group.
To join a group:
Tap the name of the group you wish to join
Tap on the orange Join group button