Is it just a matter of advertising and letting them contact you? Or do you register with your local authority? Glasgow property if it makes any difference

I would strongly advise you to rent via a property letting agency for your peace of mind, they’ll handle any problems that might arise and ensure your property is safe.
Since you haven’t mentioned contracts and legal housing agreements I think this will be your best option.
Fineholm who’s office is in Bath Street, I think, or at least one of those streets running up by Central Station on the Argyle Street end have a pretty good reputation.