As fast as 2-3 business days.
From a legal perspective, there are two steps to forming a company:
The only external factor in these two steps is that the certificate of incorporation needs to be filed with the Delaware Secretary of State. The filing takes 2-3 business days (it normally takes weeks, but we use expedited processing). Aside from that, the time it takes to form the company depends completely on how fast you do things.
If you want, you can get started on your post-incorporation setup transaction while you are waiting for the Delaware Secretary of State to return the filing. This can save you some time, since the post-incorporation setup may contain some concepts that you will need to read up on or decisions you need to think through. If you do this, please be aware that most lawyers would strongly advise against signing any paperwork (including the post-incorporation setup paperwork) prior to receiving a copy of the filed certificate of incorporation back from the Delaware Secretary of State.