Once you've agreed on the investment terms with the company in question, you can submit your investment by clicking the "Make Investment" button on the Overview or Investing tab in your fund dashboard.
AngelList will review your investment submission within 12 hours, and you'll receive an email when it's approved. Once you receive the approval email, you can connect AngelList's Venture Fund backoffice team (firstname.lastname@example.org) with the company.
AngelList then signs the investment documents on your behalf and triggers the wire to the company.
You can see these details (including a copy-able signature block and a draft email) under the button for "Closing Instructions" on the Investing tab for your Fund.