The modern concept of a hotel hasn't been around that long, but the concept of an "inn" has been around for thousands of years. You may be familiar with the Biblical story about Joseph and Mary and no room at the inn. Despite the fact that the actual events in the story may not stack up as historical, the writings nonetheless date from the first few centuries C.E. so the concept of an inn has been around a long time.

The difference between an inn and a hotel is that a hotel is just like home more or less. You get your own room, you can request different types of food, you can get your clothes washed, and so on.

An inn was typically part of the local tavern/pub. The tavern owner would have a room in the back or upstairs with a few beds in it for weary travelers. So you could get one kind of meal--whatever was on the stove. And the bed would be yours but you wouldn't necessarily be alone in the room. And any other amenities--washing clothes, and so on--you would have to take care of elsewhere in town yourself.

In cases where there was no room at the inn, or there was no inn, the local tavern owner or whoever you ran into on the street would often make a suggestion on a local resident who might have a spare room who would be amenable to an overnight guest. For example, during the American Revolution, future U.S. President John Adams often wrote in his diary as he was traveling through the country about whom he stayed with in the small towns that dotted the American countryside. Often it would be an old local militia captain from the French and Indian War who was pro-Patriot. But in any case, through his diaries, it is evident that when he stopped for the night, he very often just asked around town to find a place to stay for the night, and sometimes it was easy but sometimes it wasn't.

They would often rent a room if possible. Im ancient Rome (and I believe Greece as well) there was a big focus on hospitality- if you knew someone in a city you would usually stay with them. Something that developed from this was the tradition of exchanging 'hospitality marks' (I forgot the real name). They guaranteed that you would always take the other in, defend them from their enemies and give them a proper burial in case of their death.