Is there a need to “break in” the engine at all? Do I need to keep the speed down or limit how long I drive it? If so, why?
Read the owners manual. You will find all kinds of good information there, including directions on how to break in the car, and the maintenance schedule. Resist the urge to do “nice” things for your car like getting oil changes as Jiffy Lube recommends instead of following the manual. Just do what the car maker recommends.
What Ravenman said. Also, put only the fuel recommended in the owner’s manual into the car. Higher octane fuel is not “better” fuel, even if the idiot oil companies do advertise it as “premium”.
I do actually read the owner’s manual so I have that perspective but I’ve seen different viewpoints…
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Is it only the pistons and rings that I have to worry about? Should I not use my stereo at full volume for a few miles as well? 
don’t go towing or anything like that within the first thousand miles or so; otherwise just drive normally.
First 500 miles or so resist the urge to plant either the accelerator or brake pedal deeply into the carpet; it’s not a rental car :D:D
Modern engines are light years ahead of earlier pig iron motors. You won’t be finding shards of metal :eek: in the oil pan during the break-in period. Just drive modestly as others have mentioned. Some manuals ask for an early oil change then just regular intervals from then on. Follow the recommendations.
Another reason to go lightly the first few hundred miles is tires. New tires may still have mold release compound in the tread. This material is slippery (makes it easier to get out of the mold - duh) and will reduce traction until buffed out on the road surface. Also, the first 1/16" of tread is pretty squirmy.
You didn’t give us a make and model, but there are sometimes specific breakin schedules if a vehicle is to be used for towing. My latest purchase had a pretty detailed set of speeds, hi-throttle accelerations, etc. for the first 1000 miles (and then another set of limitations for the first 500 miles of actual towing).
Don’t know if any of this applies, but thought I’d throw it in, just in case.
Wiki answers
Ignore. Contains hodgepodge of advice from different eras and of varying validity.
Cartalk.com
Ignore. Gets it half right, but reverts to fudging with general advice that may or may not apply.
The advice so far in this thread is good. Specific instructions in the owner’s manual, or lack thereof, is the real answer for you.
In general, engine break-in as was known decades ago is essentially obsolete due to advances in engine design and manufacture and in oil formulation. Most friends, co-workers, relatives, etc. don’t know this and will earnestly give what they BELIEVE to be, but do not KNOW to be, good advice. Thank them and ignore said advice, as they are not aware of the limitations of their knowledge.