Ask an agent and have them charge a letting fee only and not retain them for ongoing management.
Doing it alone is just going to cause you problems later - you'll have no way of screening out tenants and end up with trash living there trashing your place.
Bit of a sweeping generalisation. We've done it without an agent for 30 years, and it is only the past two years that we have had an agent find the tenant, and that was only due to a family illness that needed our full attention.
In all that time, my mother and I used to do our own "gut feel" investigations. Never looked at payslips, never called for references, and in all that time we only ever had less than a handful of bad tenants.
Actually, the first time we had an agent find us a tenant they put in an ex-hooker who ended up abandoning the house. That put us off that idea for another several years. They probably saw an easy way to make a week's rent without having to deal with the dross they sent our way.
In fact, we found that many tenants (mainly older tenants not happy to be judged by a young PM having such power) were sick of being treated like rubbish by agencies and having to be judged worthy or not by a stranger that they chose to rent privately to avoid having to deal with PMs. Of course, there were also those tenants who couldn't rent through an agency due to a bad rental record, etc, but we always found those quite easy to pick.
These days though, unlike earlier years, the internet has made it almost a waste of time advertising in the newspaper, which was the only place we could advertise (until recently when a few sites made it easier to get on the main sites).
I don't suggest others do what we did, and go mostly on "gut feeling" but it very rarely let us down. When it did, it was generally due to accepting less than ideal tenants due to financial pressure to get some income flowing. In other words, our "gut feeling" didn't let us down but our need for cashflow meant we didn't listen to our gut.
We have tenants moving out soon, and we have decided to have an agent find us a tenant in exchange for a week's rent plus GST. That is another thing I found was a waste of time over many years... finding an agent who would actually find a good tenant knowing they would not be managing it. We have found a great agent and plan on sticking to this plan for the moment. I'm impressed with the investigation they do, and maybe I'm just over doing it myself.
