The term you're looking for is print and play. There's a very large print and play community out there. Websites dedicated to sharing games. The board game industry is pretty open source as game mechanisms are not copyrightable. Only art and rules can be copyrighted.

https://www.pnparcade.com/collections/free-games

https://boardgamegeek.com/boardgamecategory/1120/print-and-play

Assuming you're in the U.S. (though possibly even if you aren't)...

The cool thing about game mechanics (boardgame, video game, school playground game, etc) is that they're not covered by copyright. And (while this bit might be less true of video game mechanics) they're rarely covered by patents.

So, for the most part, clones require no licensing or anything. You can make a knock-off of Carcassonne or Settlers of Catan or whatever legally, so long as you avoid trademark infringement. (Basically as long as you're careful to make it clear your game isn't by such-and-such company and you don't have any affiliation with them.)

(Also, it's worthwhile to mention that some games are as much or more so "flavor" as/than mechanics. In such cases, while I don't know that there has been that much precent in the court, it's likely the flavor would be considered copyrightable. So maybe if you're copying the BSG boardgame, don't include Cylons. Also, IANAL.)

I once designed/manufactured a 3d-printable clone of Cubed: Next Level Dominoes, which itself was a(n I'm pretty sure unlicensed) clone of The Grid Game.

https://www.cardsagainsthumanity.com/

It's available in multiple language for download too I believe.

Download link for the PDF is on the main page

Secret Hitler is CC 4.0 and is really fun. They have a print and play version you can download on the website for free.

Parcheesi is public domain, easy to grasp, and supports four players.