You can join one object or group into another with the Join Tool. There are two ways to access the Join tool:
Run the Join command first
Keyboard: J G
Run the Join command and follow the mode instruction in the upper left of the screen
Single click to Select an object to join into
Single click to Select an object(s) or group(s) to be joined
Click the check mark to finish the command.
Select objects first
Double click to select the object to be join. (Single click for a group)
Holding the CTRL key double click an overlapping object(s) to join.
Right click on any of the ojects and choose the Join Tool in the Context Menu