All onsen in Japan will contain at least one hot bath, perhaps several baths, ranging from cold, to warm, indoor or outdoor [picture above, a rotenburo]. Move freely between the baths, but DO NOT put your now disgusting, foreign bacteria-filled towel into any bath. Many Japanese put the towels on their heads. If not, putting them beside the bath is acceptable.
If you wish to soap, wash and rinse and return to the bath again that is perfectly fine.
After soaking for as long as you wish there will probably be hairdryers, hair brushes and various Japanese body lotions in the dressing room. Enjoy!