After a nearly 25-year hiatus, and after moving back to near where I grew up, I decided to start playing TTRPGs again with 5e in 2015. I created my own homebrew world and campaign and ran a couple adventures for a couple of old high-school friends that I played with in the 80s. Unfortunately, there were not enough old friends left in the area who were available to join a regular campaign. So I had to go and find players who would be strangers to me. Something I was cautious about because I run the games from my home.
I started by posting a notice to a couple Meetup.com sites for local TTRPG players. I explained my campaign, my strange approach to scheduling, a bit about myself, what I was looking for in players, and some home rules and house rules. From the responses I would e-mail the interested players and we'd discuss the campaign to decide if it was a right fit. I found that the player who were vetting me as much as I was vetting them turned out the be the best fit at the table.
That led to two additional players. Additional or replacement players over the past five years have been recommendations from existing players, but even with these, I would discuss the campaign and their characters by e-mail.
I've yet to have any horror stories with players. Those who left, left primarily because of time conflicts.
An example initial post or e-mail to a potential player would go something like:
I'd start with a call for players and a campaign pitch. E.g.:
It has been four centuries since the Great Wars and the driving out of elves and arcane magic from the known world. From the ashes of numerous kingdoms arose the eight great human and dwarven realms that have joined together in a federation whose members' vast rule covers nearly all corners of the known world. Still, even four hundred years has not been enough time to recover from the devastation of the Great Wars.
Whole cities and even kingdoms have been reclaimed by wilderness and ancient threats barely remembered in myth are rumored to have returned. Moreover, the bonds of brotherhood among the peoples of the federated realms have grown slack and frayed from lack of need—replaced with threads of intrigue. Perhaps the stirring threats from the cold wastelands—orcs from the west, goblinoids from the east—will cause the peoples of the Federation to tighten and once again hold fast to the bonds that saved them from obliteration four hundred years ago.
What role will you play? Where does your destiny lie? Join us in our campaign: The Federation of Eight Realms.
A description of our group's weird scheduling. We are all working professionals and have to be flexible with scheduling.
We meet once per month on a Saturday, from 10am to 6pm. The exact Saturday changes from month-to-month. I know that can make it tough to commit to a campaign, though most of use make all the sessions. Still, I try (though I'm not always successful) to have each session be a complete adventure, so if you must miss a session you can without leaving anyone hanging. Also happy to have "guest stars" if you want to join occasionally, playing an pre-generated character or creating a character just for that session.
For players who joined after a campaign is in full swing, I'd describe the current group of players and I'd give a far more detailed campaign description and the adventure(s) so far, followed by guidelines on character level and start a discussion on what kind of character they want to play based on what I've told them about the campaign. This allows me to work them into to the campaign. If there are any character class or race restrictions I'll specify that. For example, in my first campaign only humans, halfings, gnomes, and dwarves could be played and the only arcane magic users allowed were sorcerer's. After two years of my home brew campaign, I ran Curse of Strahd and allowed any official WotC character option. My current game is the 5e version of the Rappan Athuk, which is more kitchen sink and borderline gonzo.
Next I would describe House Rules, e.g.:
Will use D&D 5th Edition.
Multi-classing under the 5th edition rules is allowed.
Elves, Tieflings, and Dragonborn are not allowed as a player races. Half-elves and half-orcs may be allowed if convincing backstories are created and they are not visually identifiable as being part elven or orcish.
Wizard, Sorcerer, and Warlock are not allowed classes at first level.
Non-magic variants of Rangers and Bards are used (using rule variants published in an Unearthed Arcana article for Rangers and home brewed Bard class).
You can role once for ability scores. If you don't like your role, you can use the "Customizing Ability Scores" variant (PH 13) where you have points to "buy" certain ability scores.
Players will bring snacks and drinks to share with the group.
Characters level up every session.
Finally, I would note any technology used or required. Originally, there were no requirements. But eventually I required that players created characters in DnD Beyond and add them to my campaign in DnD Beyond. It is free to the players, so no objections. Currently, we have to play remotely, so everyone has to use Foundry as our VTT, but again, there is no cost to the players and they don't have to download, install, or configure anything.