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 Investments pages in your fund dashboard.
AngelList will review the deal within 12 hours, and you'll receive an email when it's approved. Once you receive the approval email, you can connect AngelList's backoffice team (email@example.com) with the company.
AngelList then signs the investment documents on your behalf and triggers the wire to the company.
You can see these details and a draft email at the bottom of the Investments page in your fund dashboard.