First, the Clerk's Office will notify you if there are any defects in your application. The Clerk was the one who set the notice date and entered it. A response by the other party must be filed by the notice date in order to be considered. If they file a motion for dismissal or a response to your application for leave, you are able to file a response (10 pages or less). The Court generally will not entertain a motion to dismiss, however.
But, other than that, it is out of your hands. You do not attend any hearings unless the Court decides to hear oral arguments - and that is still a long ways off and very iffy.
You will be notified by the Court if there is a conference on your application. Conferences are scheduled if one or more of the Justices has objected to the recommended order by the Commissioner, or because the Commissioner has recommended a conference, or because a conference is needed to grant leave to appeal or peremptory relief.
At a conference (and, again, only a third or so of cases will make it to conference), the Justices will decide what action to take. It could be to ask for the opposing party to respond to the application, if they have not already done so, or it could be to ask for a further analysis of the issues, or it could be to place the case on the session calendar for oral arguments to be heard.
The oral arguments are usually heard on only selected issues that the Justices may need clarification on. If your case is selected for oral argument, both you and the other party will file supplementary briefs. Following oral arguments, the Court will again consider the application for leave to appeal, and will make their determination.
If the majority of Justices are inclined to grant a leave of appeal, another separate conference is held on that, to make a final determination.
But, jci, you are a LONG way off from that right now. The first step will be to answer any motion or response the other party may submit. And then you wait.