Bowling Pins are a pretty informal competition. Seems every range has their own way of running the match.
In General:
there are 5 pins on a table around 20-25 feet from the line.
Shooter loads and makes ready, buzzer sounds, shooter engages pins.
Table has to be clear of pins to be completed.
Common Variances:
placement of pins for different calibers. eg for big bore, front of table, 22 back of table.
some places only judge hitting the pin, don't have to clear the table. This is usually out of concern for either safety, or damaging the table.
Time is usually shoot 4 tables, drop lowest score, average the other 3. But I have seen various ways of scorig time.
Give it a try! Pins are alot of fun, I especially enjoy shooting them with a .22. Shooting fast is fun!