How do I set up a contest on my own URL?

There's 2 options, you can set-up a subdomain or you can use an embedded landing page.

Here's how to set each up: 

Subdomain:
https://vyper.zendesk.com/hc/en-us/articles/360001518211-How-do-I-add-a-subdomain-to-my-contest-

Embedded landing page:
https://vyper.zendesk.com/hc/en-us/articles/360001516251-How-do-I-embed-a-contest-on-my-own-domain-use-the-embedded-contest-form-aka-my-own-landing-page-