bgf, in college football, offensive players are allowed to block downfield while the ball is in the air if the ball is caught behind the line of scrimmage. In the NFL, you are not allowed to block downfield while the ball is in the air regardless of where it is caught.
I think the ESPN writeup is a good one which covers the basics common to most NFL teams.
With more teams playing a spread offense, we see more middle screen which is similar to the bubble screen, but instead of being executed to one side of the field or another, the receiver continues his route to the middle of the field and then follows his linemen up the middle of the field..
Some teams are good at running screens and others are not. Obviously, personnel may be a factor in it. I can't recall a time when the Giants ran more screens, with more success than during the brief time when Kurt Warner and Tiki Barber were paired in the Giants backfield. They continued to run them with Eli, but to a lesser extent, and after Tiki with even less frequency. But, whatever the personnel, the real key to success is having a commitment to it as an integral part of your offense. It takes a lot of practice for the players to be able to execute them well and with confidence, and for an OC to be comfortable incorporating them in his plan and in calling them.