Having "difficulty" with one of those two functions (channel selection, mute/volume) that never work, or work intermittently? Or "nothing ever works"?
The channel-changing is done by the Shaw TV box -- feeding a different channel into your TV. So, you have to "point" your remote-control at the Shaw TV box. Older Shaw-supplied remote-controls were very "picky" about your aim. The Shaw-supplied remote-control for the Shaw Gateway device is quite forgiving about "pointing".
The mute/volume control buttons on your remote control require that you program the remote-control to correctly send the infrared signals directly to your TV, so that the TV does the commands. You have to "point" your remote-control at your TV's infrared receiver (which might be in the bottom-left or bottom-right corner of the surrounding cabinetry).
So, which remote-control device(s) are you using? Which Shaw TV box do you have?