Hey allen. Congrats on you first, rewarding step! Well, if you just turned in your petition and the next stated meeting is tomorrow then you may or may not hear something immediately. During the next meeting they will formally accept your petition and assign an investigation committee. You may hear from them right away or they may call you individually, depends on the lodge. Then the committee has a month to visit with you and write a report. At the next stated meeting following the this coming one, they will vote on your petition.
EDIT: So basically game plan on 1 month + 1 day (give or take) until the petition vote. In the meantime, I encourage you to go to meetings and get to know the brothers. You won't be able to sit in an open lodge with them yet, but that doesn't mean you can't fellowship beforehand. These men will grow to be close to you, take this time to get to know them better.