First off, what did you buy? In particular, what blade?
General advice (without having more information): Proceed with caution. Many pro-shops specialize in hockey skates and do a horrible job with figure skates. One sloppy job of sharpening can destroy a pair of figure blades. Are you taking lessons? If so, ask your coach or instructor for a recommendation. If not, look up coaches at your rink, or figure skaters that you see on the ice, and ask them whether they trust the local pro-shop or go elsewhere. One parameter you need to specify to the sharpener is the radius of hollow (ROH). If you don't know (and don't have a coach to talk to), then I would recommend starting with 1/2". If the sharpener asks "What's ROH?", go elsewhere.
At some pro-shops, there may be more than one sharpener, but only one who does figure skates properly. But if you just drop off your skates, you might just get the next available guy. You then need to specify, I want these sharpened by Rich (or Bob or Ken or whoever the right guy is ...). So when you ask for recommendations, clarify whether you need to specify a particular sharpener at a particular pro-shop.