Shipping package question!

I have only ever taken my package into the post office and paid for postage there. I went in yesterday and the employee entered the wrong measurements, which more than doubled what my shipping cost should have been. I did not realize that until today and now I'm wondering how many times in the past I have been screwed over.

So now I will be measuring everything myself and printing my own label. I have never done this before, so my question is, once I have my postage paid for, label printed and on my package, everything is ready to go, what do I do? Do I still have to go to the post office and wait in line and just hand it over? How does this work?