How common is breaking a spoke?

If it's a relatively new or low-miles bike then breaking a spoke on a normal ride is pretty unusual, but not too unusual for an older bike.  Spokes tend to get stressed, especially right at the hub, and will break over time.  And once one breaks, it's not unusual for others to start breaking as well.

Mechanics of replacing a spoke are pretty simple, just a question of making sure it's laced the same way the old one was, going over and under the other spokes the same way.  But getting the tension right is probably beyond the skill of a casual bike mechanic, and will be further complicated if the wheel is slightly out of true (like, from being ridden with a broken spoke).  I do a fair amount of my own maintenance, but this is one I'd take to the shop.

Not uncommon on the rear wheel as it carries most of the load.  Much more uncommon on the front wheel.

It really depends on the wheel and how big the rider is.  My first tri bike I had 3 or 4 spokes break...I finally had my LBS make me a heavier wheel.  I was about 260 lbs.  My next tri bike, a Felt B12, I am still on the stock wheel and have never had a spoke break despite being 20 lbs heavier.  The B12 has bladded spokes....not sure how much of a factor that is.  I 'spect spoke count is more important than the type of spoke but both are factors.

You can fix it youself but truing the wheel is like tunning a piano....you can do it yourself but it's probably better to let someone who does it all the time to do it for you.  It is not expensive.

~Mike