Checking references should be straightforward but like a lot of aspects of hiring it’s conceptually easy and practically difficult. Some individuals will deliver references at the drop of a hat but an increasing amount won’t.
Obviously if the candidate has worked with companies you know then this could be straightforward but when they haven’t then dig in and try and dig deep. Taking references face to face is great though rarely practicable. Taking them by video call or telephone is the next best thing. For best effect speak to people above, below and equal to the individual being hired. Customers, Suppliers, Contacts could all be relevant depending on the role so don’t always think inside the business is the best place to pick up references. It’s often others that will give a more honest view.
Check dates and titles as par for the course and check facts gleaned in interview (without sounding like your hunting for issues) and leave it open for referee’s to give more than you’ve asked for.
Put confidentiality at the core of what you do in reference checking and remember you might just be getting opinion rather than objective insight. So if it doesn’t turn out quite as well as expected ask what the circumstances might be that made that happen. It’s not necessarily good but it’s not necessarily bad then either.