Publishing your game is easy. Just go to the File menu and export it as an executable file (.exe)
This will generate a file that anyone on a windows PC can download and play. You're then free to upload that file anywhere you like. Three popular options are host-a.net, gamejolt.com and itch.io.
Once you've done that, you can share it on the The "Made with GameMaker" board by posting a link, a description, and some screenshots.
Let me know once you've done that. I'd love to play it.
Lastly, have you tried GMS2? If you upgrade to the latest version there are no pesky watermarks and you gain access to loads of new features. Might be worth considering.
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By the by, we have a Game Jam coming up this weekend. If you have some free time and want to try making another game, it's a fantastic way to challenge yourself and learn new things. The more the merrier!