New York State requires that all trailers be registered and inspected regardless of weight. Per this web page, the fee should be under $15.00/year (plus whatever hidden surcharges DMV wants to tack on): http://dmv.ny.gov/node/1967
If you bought the Harbor Freight kit or a small landscaping trailer at a big-box store, make sure that you get the MCO (Manufacturer's Certificate of Origin, aka: title) and a receipt for the purchase price that shows whether or not sales tax was paid. If the tax wasn't collected, you will need the original receipt at DMV to pay it there.
You may also need an official scale receipt to document the completed weight if it is not on the MCO. Per NYS law (that a lot of people and cops do not know), you can tow an *empty* trailer to/from a scale without a license plate for the sole purpose of having it weighed prior to registration.
There are also instructions on the web page above if you want to register a home-made trailer. Save *every* receipt for parts, as they will ask for them at registration time.....