It's pretty straight forward. Use ATF E-forms to complete a form 1 submission. You will attach a passport like photo to the submission - if you don't take your own, CVS will do it, just get the emailed image in addition to the paper photo. You'll pay the $200 tax when you submit the form. Within a short period of time of your submission, you will get a confirmation from the ATF that it was received, you need to mail that confirmation along with 2 finger print cards to the ATF processing office in West Virginia. Once it is approved, you need to get the lower engraved with your name, and location i.e. Harrisonburg, VA in my case. If your lower doesn't specify the caliber, and the barrel doesn't clearly indicate it either, have the engraver mark it 5.56 mm. Once the form is approved, mail a copy of it to your local chief law enforcement officer. Once you've done these steps, you are clear to add a rifle stock in place of whatever your pistol receiver extension is. Keep in mind that with an SBR, before you cross state lines with it as an SBR, you need to notify the ATF, and get their approval for it. It's a form you submit, and you can submit them for a 1 year period at a time to go to a specific state.
PM me if you have further questions. While it sounds complex, it's actually pretty easy.