First you need to have the repository already downloaded and managed by HACS.
Once that is in place, click on the card for the repository you want to enable beta releases for, and click the 3 dots in top right corner to bring up the repository menu.
In that menu click on "Redownload" to bring up the Redownload dialog.
Activate the checkbox to the left of "Show beta versions", once you activate that HACS will fetch new information in the background, once that is done you can now select a beta version to download.
Not all repositories will have beta releases, it is up to the author of the repository to use that.