Note that Avid refers to the shots in your sequence as both clips and segments. So, don't let that cause you any confusion.
In order to set clip colors in the Timeline Window, you must first enable their display. Go to the Timeline Window Fast Menu (the hamburger-looking icon in the bottom left-hand side of the Timeline Window) | Clip Color | Timeline Local.
Select a clip in the Sequence by using either of the Segment Mode Arrow tools (it doesn't matter which one you use). To select multiple segments, hold down the Shift key as you make selections. Alternatively, you can also select segments by lassoing left to right around one or more of them, or you can use the Select Left, Select Right, or Select In/Out functions.
Once segments are selected, set the color with one of the following methods:
Go to Edit menu, Set Local Clip Color, and make a selection from the palette
Right-click in the Timeline Window, choose Set Local Clip Color, and...