To invest on AngelList, you need to be an accredited investor, and you need to have been approved to invest. You can fill out the investor application here.
Once approved, you can search for syndicates to join. Navigate to the All Syndicates page in your Invest dashboard. There you can search or browse all public syndicates.
Syndicate leads may also invite you directly to their syndicate by sending you a link to their public syndicate profile. You can click the "Back Syndicate" button to apply to back a syndicate.