Is it significantly more expensive than ordering similar products from Amazon?
That can vary. Some things will be cheap as heck. Like I can print a (plastic) shelf bracket for about a dollar or I can run to a hardware store and buy one for $8.
I'm currently printing a cat feeder to slow down my piggy-cat. Overall, it is probably going to cost me $40. I downloaded this feeder and printed it once already. I'm not satisfied with it. The original design looks nice and the person that made it obviously knows how to make nice looking parts. However, (s)he didn't consider limitations of 3D printers and it is far more difficult to print than it needs to be. There are also fitment issues, so I'm redesigning most of the parts and printing it a second time. Alternatively, I could have bought this one
A part printed in 3D isn't typically as strong as a part molded from plastic, and it often has visible artifacts that keep the surface from being smooth. Most printers can only do a single color, but there are many that can do two and several that can do more. Mine can do five colors.
As for where do you go to do the printing, you'll either use your own printer or you'll have to go to an online shop such as ShapeWays. ShapeWays and similar shops are quite expensive for what you get if want something like a rain guage.
There's a much bigger part (or category of parts) I print for work. I basically get paid for it in printer parts and filament, but I'm curious to see how I'm making out...
For printing 4 of these parts, I get "paid" in about $250 in filament. Each part requires about $15 in filament, so I'm making $190. I just loaded this thing into ShapeWays, and they quoted me $600 each for a single color print so I lose all of the text, serial numbers, part numbers, instructions, etc. I need to negotiate for more filament!