This works just like how you would start a normal friendly challenge. As with friendly challenges, it is useful for testing a new base layout or a new army before actually attacking in a Clan Capital raid. To do this, simply go to your Clan Capital, and then go to the district that you want to challenge. Then start the challenge, and it should appear in the clan chat as shown below. The red trash can icon below will cancel the challenge.
After that, you can attempt to attack the challenged district like you would to districts in Clan Capital raids, being able to scout, attack, and change your clan capital army like normal. As someone attacks the district, you can see the attack progress on the base as you would in a Clan Capital Raid. Below shows a fully destroyed district from a challenge.
If you want to see the clan capital bases, tap or click on the link below or type in this clan tag: #2QC0808PU