It is important to put your hand in the strap correctly, you do this by putting your hand through the loop from underneath, enough so that loop goes to about the wrist, and then grab hold of the handle. When the strap is the correct length it should allow you to grip the handle comfortably. Too short and the strap will feel tight around the wrist too long and you will feel no support. The trick here is not to hold the handle too tightly, let the strap do the work.
Adjusting strap length
If you need to adjust the strap length you can do this by pulling the strap that has the small plastic wedge, this then releases the other strap so you can either make it bigger or smaller.
Adjusting the length of your trekking pole
The next thing to adjust is the pole length. The pole is made of three sections with each joint having a small plastic wedge that when you twist the smaller pole clockwise tightens and anti clockwise loosens it (see diagram). Set the lower section to the "Stop" mark and then adjust the length of the pole so that when you are holding pole you elbow is at 90° to the pole with pole hanging straight. You may find that on soft ground particularly snow the pole sinks in (even with the basket on) and you may need to adjust the length to maintain the correct angle.
It is also best to adjust the trekking pole length to suit the terrain. On accent you could shorten the pole and on descents lengthen it or just use the palm of you hand on the top of the pole. When traversing a slope or on a zig zag path it maybe be best to have one long and one short and swap them at each turn. But just remember you supposed to be walking not adjusting you poles, but when you need a rest on a uphill slog it is always best to have something technical to adjust rather than blame your fitness.
So your hands are in the strap correctly and you have set the pole length just how you like it, How do I actually use them. Good question.
Firstly don't grip the handle to hard, it is the strap that should be doing all the work. Have a relaxed grip that allows the trekking pole to have natural swinging action. You should use opposite pole to the leading leg, so right pole left leg and vice versa. The position of the pole plant should be roughly level with your foot but it's what ever suits you.
It is important to remember the limitations of your trekking poles, especially when the terrain gets tricky. Very often it is best to pack the poles away which allows you to use your hands to better advantage.
In this video I give an overview of the Compact Ultra trekking poles including how to set them up, adjusting them and how to use them.