Hallo,
if you are officially married, you have right to be transferred to your wife during your asylum procedure, you must apply for this in your Ausländerbehörde. From there your application will be sent to the Ausländerbehörde in the place where your wife lives and they must give their agreement. How long it takes nobody can know or perhaps only those who have experience with the both Ausländerbehörden. Your wife can try to speak with her Ausländerbehörde to speed the decision up.
If you apply for a residence permit because of your marriage and family reunion, it is really not so easy. You came as an asylum seeker and for another residence aim you normally must make a visum procedure. If your case is without some special hardship (little children, sicknesses), the Ausländerbehörde would probably insist on making a visum for family reunion in a German embassy. But if you have no international protection and no residence permit in Italy, I don't know if you can do it from Italy at all. Then it must be an embassy in your country.
If you don't come to an easy agreement with the Ausländerbehörde about issuing a residence permit and refuse to go and make a visum, it is essential to have a good lawyer for alien law. Also try to find a good councelling center in your or your wife's place.