Keeping in mind that a dull tool is not only ineffective but dangerous as well, sharpening is an important part of woodturning. You cannot "send your tools out" to be sharpened... you sharpen/hone as you go. It is not uncommon to re-sharpen (hone) your tools a half-dozen times or more as you work on a project.
However, these are not carving tools, and do not require a highly polished and honed cutting surface. Remember, we have a motor driving the wood into/along the tool edge, and are not relying on muscle power.
That said, turning tools are best sharpened on either a belt or a wheel. If you use a wheel, remember that the larger the wheel diameter, the better for the tool. 8-inch wheels are good, 6-inch wheels are much less so. So turners sharpen on a belt... this is O.K. Some turners (I call them "old-school") learned to sharpen by hand and are very good at it; this is difficult for the beginning hobbiest turner to master, which is why jigs were developed and are recommend.
There are a number of schools of thought when it comes to the grit (coarseness) of your sharpening wheels, as well as the composition of the matrix (identified by color: gray, blue, white, pink, green). Good results are obtained with 120-grit 8-inch pink or blue wheels. Gray wheels are for lawn mower blades and shovels; green wheels are for carbide tools only.
Woodturning is the most fun you can possibly have with your clothes on and not get arrested (usually)!