Once you are ready to share your Roblox project with the world, it is really simple to publish it.
Click 'File' in the top left corner of Roblox Studio
Select 'Publish to Roblox As...'
The next step depends on whether you are publishing a new or existing game.
Publishing a new game
If you want to publish your project to a new 'game', you can fill out its basic information here and click 'Create' to publish it to Roblox.
Publishing an existing game
If you want to publish your project to a game already published on the Roblox website, you can instead click 'Update existing game' in the bottom left corner of the Publish Place window. This will open a list of all of your published games, allowing you to select one to publish to.
Where can I find my published game?
All of your published games can be found in the 'Create' section of the Roblox website under 'Games'. Click here to go straight there.
How can I make it so other people can play my published game?
Published games are 'Private' by default, meaning only the person who created them can play them. If you want to share your game with other people, you will need to make it 'Public' first. The quickest way to do this is:
Find your game in the 'Create' section of the Roblox website (link)
Select the little gear icon on the right hand side of the game (see image below)
Click 'Configure Game'
Check the 'Public' option under 'Privacy' and then click 'Save'
Once this is done, other people with a link to your game will be able to play it!