How do I offer a service-only item for sale on my website with no shipping, etc?

Simply add the item into your web-based admin product manager and set “Charge Shipping For This Item?” to “NO” and then set the product weight to 0 (zero). 

The item will now be excluded from any shipping calculations.

Also, if you will be offering the item as labor (example: installation, support, etc), you will probably want to set “Charge Sales Tax?” to “NO” as well.  Typically you would not want to charge state sales tax on service (labor).