Congrats! As to what happens next...after the order is confirmed, a Delivery Specialist will be assigned to you. His/her contract info will show up in your my tesla account, and most likely they will get in touch soon. When they do they might be able to give you some more details on a scheduled production date and approximate delivery timeframe (the ones in your my tesla account will change, and possibly be inaccurate, but the info my DS gave me was spot on).
Also they will guide you through finance or lease options and trade in details.
If it hasn't already, a section will appear in your my tesla page to upload copies of required documents such as your drivers license and proof of insurance. You will also begin to see documents such as owners manuals and required disclosures appear there.
After that, apply for financing (if your going that route) at the time given by your DS. Financing approvals only last about 30 days and vary by lender, so make sure your delivery range is pretty set before applying.
Finally, schedule a delivery date! Delivery is pretty straight forward. Only one signature was needed for us at the showroom. Any financing and down payment should be handled by wire transfer before you show up. Since I live outside of CA, they fed exd me a temporary registration and associated paperwork the week before. The day of a Tesla rep will guide you through an inspection and explain the features of the car as well as help fix any issues on the spot or compile a due list to be done later.
Hope this helps. I know I read a few bad stories on here about issues people had, but my purchase process was nearly flawless.