Bring two water bottles and a snack. Then just do it.
When you first start riding you will be sore. Especially your butt, because you're probably not used to sitting on a bike seat for very long. When I first started riding I didn't have any problems with my legs being sore, but my shoulders were. That's because I wasn't used to riding a road bike or was doing something weird with my arms or shoulders.
If you're kind of in shape you should be able to ride for an hour. It's just like doing a moderate exercise for an hour (depending on your pace). If you keep increasing your distance, soon 10 miles will only seem like a warm up.
You mention that you just started riding your bike, you get used to using "cycling muscles" which will make it easier.