Disclaimer: I own exactly one rental property and have rented it exactly one time. Here's what I did.
1) I advertised mine on Zillow, Trulia, Hotpads, and Craigslist. I also have my own Web site, where I put a couple of the listing pictures and a link to the Craigslist ad. I also put a sign in the yard that just said "House for Rent", my website, and my phone number. I got hits from all of these methods.
For the online ads, I borrowed a camera and a tripod. I tried using my own point-and-shoot camera, but it wasn't wide-angle enough (the numbers on the lens are "6.7-24 mm") to capture all of the room. The camera I borrowed was wider-angle (smaller number on the lens was "4 mm") and worked better. I also picked a sunny day and shot different rooms at different times of day, depending on what side of the house they were on. If you can, look at the photos on a bigger screen (not the back of the camera) soon after you take them, so you know if you need to re-shoot or not. I also put a copyright notice and the property address in text on each photo before I put them online.
For the sign, I did the artwork myself, uploaded it to Staples, and had them print and ship it - they were the cheapest that I found at the time (mid-2017) for small quantities. If you don't want to do your own artwork, they have some "canned" designs that you can use by filling in your phone number and URL if you want. You can get a double-sided corrugated plastic sign that will come with a cheap H-shaped wire post. I had a slightly sturdier signpost that a roofer had used at my residence, so I ordered two single-sided corrugated plastic signs and attached them to both sides of that post. My rental is a suburban house with a front yard; if yours is in the city and doesn't have a front yard, maybe a sign in the window or on the front of the house would work better.
I got replies via email, phone, and people knocking on the front door. I found it helpful to keep a spreadsheet with the person's name, phone number, email, source (which site they saw it on), and if they wanted to stop by the open house, what time I proposed to them. A couple of the door-knockers were just neighbors who were curious, but I showed them around the house anyway. (Sometimes neighbors have friends and relatives that are looking for a place to stay!)
2) I added a clause for most of the appliances that says, in essence, "if it breaks, I will replace it, but it may not be exactly the same as what is there now". My thinking was that if (say) the 20 cubic foot fridge goes out, and all I can find for purchase today is an 18 cubic footer, then the lease lets me use that slightly smaller fridge. For a couple of things, including the garbage disposal and the storage shed that was in the back yard, that clause also says that I may not replace it at all.
Check with a lawyer on this, because it may not work in all states, but: I put in a clause that says the tenants waive their right to a jury trial. They can still go to court, and have a lawyer if they want, but it would just be them, their lawyer (if they have one), me, my lawyer, and the judge. The reason for this is that trials with just a judge happen quicker; if they ask for a jury trial, it gets scheduled a few weeks from now, which may not be what you want.
I have a clause that says that any vehicles kept at the house have to be licensed and insured, and if one becomes inoperable, it has to either be put in the garage or removed from the premises within a reasonable amount of time. It's in the kind of neighborhood where nobody cares if you do an oil change or brake job in the driveway on Saturday, or if the car has to sit until payday, when you can go to the car parts store, but I wanted to have something to cover me if they have a dead car sitting there for weeks at a time.
3) There were a couple of steps in my screening. I had an application that I asked tenants to fill out. I called and talked to previous landlords myself, and looked at what the tenants provided for employment verification (pay stubs, etc). Once I had a candidate from that screening, I used Cozy.co to get a credit report and background check. The tenant pays Cozy for the reports and the results come to me; I don't have to handle the tenants' Social Security number or bank information. The tenant does need to have some kind of Internet access to do this - they can do it from a computer, phone, or tablet. (I also use Cozy to collect the rent - it comes out of the tenant's bank account and into mine - but you don't have to; you can just use them for the credit and background check if you want.)
I am not affiliated with any companies mentioned.
I hope this helps!