For new inliners looking for a free lesson in how to stop, the Central Park Skate Patrol hosts a stopping clinic at the West 72nd St. entrance to the park on Saturday afternoons during the prime skating season from mid-April to mid-October (but probably skipping Memorial Day and Labor Day weekends).
The Skate Patrol also offers beginning and intermediate inline skating lessons at a fee. In summer 2016, lessons were early Wednesday evenings and met at the West 72nd St entrance to the park. More details are on the Skate Patrol website, as well as a calendar on their Meetup page.
As noted on the group skates page, the Skate Patrol also does a casual group skate on the Central Park Loop on summer Thursday evenings that newer skaters may find enjoyable.
Perhaps the oldest skate school in town is Joel Rappelfield's Roll America. Joel's been teaching inline lessons since the late 1980s. Call them at (212) 744-4444 or check out the Roll America website.
Another possibility for inline instruction is personal trainers who also offer skating lessons. See for example, Weights & Skates.
The SkateIA (see below) website includes a search tool to find local certified instructors. Amongst those listed for New York City in mid 2017 are Bill and Deb Harley, Sonic Shah, Maria Dubischeva, and Jonathan Ortiz of GO! Sports.
Fliers from individuals offering private instruction might be found on bulletin boards at fitness centers and sporting goods stores. Be sure to check whether the instructor cites any qualifications, specifically whether they are certified by Skate IA.
In the early days of inline skating, the only certification process for inline instructors was provided by the International In-Line Skating Association. IISA essentially closed down in 2004, and eventually an organization called the United Skate Schools Group (USSG) formed to fill the same need as the IISA instructor and certification program. In 2009, USSG was sold and renamed as the Skate Instructors Association, aka Skate IA.
Skate IA remains active as of 2017. Much like the old IISA program, Skate IA has two levels of certification. Level I means the instructor can teach the basics, and Level II means that she knows how to teach more advanced skating maneuvers and tricks. Additional special-topic programs may be available depending on the instructor. Skate IA also offers instructor insurance.