I don't have experience with 3D printing services, although I am sure somewhere would be happy to do it for you. Maybe a college in your area has one you can pay to use? I believe the majority of 3D printers are owned by companies and schools and used for design and rapid prototyping purposes.
My suggestion is to google "Rapid Prototyping" and also your area to see what services are available.
The major steps in 3D printing are modelling, preparing the model for printing, printing, and then cleaning up the print. I have done 3D printing in the past, and started by modelling my part using a 3D-modelling program (I used Pro-Engineer Wildfire). After that, you have to convert the files into a format the printer can use (STL aka stereolithography files for the printer I used). Now that you have a file that the printer knows how to print, you can print your 3D object and then remove excess material/clean it up.
3D printing can be nice for doing art, and making prototypes. I wouldn't trust it to make something durable though, although print quality may vary depending on the machine and materials it uses. Also, be wary of the $$$ factor, as I have heard stories of people doing limited runs of items on a 3D printer, and it costing a lot.
Now I am curious what you are designing
Good luck with it!