Window menu and pathfinder (panel). Go to it, select two or more paths on art board, click one of the buttons such as 'unite'. You can also find the functionality now on the properties when selecting multiple objects.
shift key + cmd / ctrl + F9 (or alternatively make your own shortcut, if this does nothing or is not memorable)
Select two or more paths. It works with one in some cases such as the outline but it works best if you are using it with multiple paths.
The first one is the Unite and you will then just combine the two paths.
The second entry is minus front and click that to remove the last path added (or the one in front) and the original path will be chopped by the overlapping top path and the top path will also go.
The next one is the intersect and where paths overlap, the intersected path will remain but the rest will be deleted.
The next button is exclude and that is the inverse of the intersect and the path's overlap will be deleted and the rest will remain.
The divide (next row) splits the paths up where the overlap is. If there is no overlap then there will be no divide. All the paths will remain but they will be broken apart depending on the overlap. You will need to use the object menu and ungroup.
Trim is similar to the minus front and unite but depend on color of the paths and if they will merge or subtract from the first path.
Crop is similar. It is easier to show the use of the crop / trim etc via the video at the top of the page as this does depend on location, fill color etc
If you have two or more objects and overlap. When you merge them and they are the sane color then they combine (though sometimes nothing happens, go figure). If they are different colors then the objects will be cut away from the top objects but all the objects remain. They are all part of the same group. You can use the direct selection tool to select and move things around to see the cutout.
The outline just creates an outline (no fill and no stroke though it remembers the fill color in the stroke color even though by default it is set to 0pt but you can always change the value afterwards to 20pt etc. The stroke is similar to the divide but instead of fills etc you end up with open paths / strokes only taking the top path's color if there is any overlap.
Minus back is similar to the minus front (it just subtracts the back instead of the front)
Click the expand if you have used the make compound
There is also functionality for live effects in the effects menu and you can find out more info about that via the graphicxtras channels on our youtube channel.
If you go to the right side menu there is some functionality such as precision. There is a repeat command which repeats the last used, though not sure of much benefit as it is easier to click the button itself.