First of all, I would like to say that while training is not mandatory to get a permit, you should get it anyway. Even if you have hunted and gunhandled all your life,you should learn the basics in carrying. Most local indoor ranges can provide the classes you need. To get the permit apply at your County's Sheriff's dept.
Every county has different criteria.
In Chester County you need to have a doctor's approval. In Delaware County you do not. The law specifies a maximum of 45 days for the entire process. When the Sheriff reaches a decision you will be notified by mail. If you are disqualified, you have the right to appeal.