Invite a musician to perform, set a date and invite your friends. Most musicians will work with you on compensation. Because some hosts are uncomfortable with inviting friends and then asking them to pay a cover charge, a large jar can be placed so people can give free-will donations. It is normally the host's responsibility to bring the donations jar to the audience's attention.
Many house concerts begin early with a pot-luck meal prior to the concert.
Some house concerts have been going on for decades. Many such organizations began during the Great Depression, grew in popularity, then moved out of homes and into larger concert venues. Some concerts are regularly hosted at the same residential location and are open to the public. Of course, that's not for everyone, but there are many such locations to be found. There are many places to learn more about hosting a house concert.