1. Find your project folder and zip it (I'm not sure can you exclude some files for Unity, but zipping the whole folder is sure way to do it)
2. On itch.io, open the menu next to your account in upper right corner. There should be Upload new project option.
3. Fill out any necessary info and add screenshots if you want (recommended).
4. Upload your zip file. Set it as "Source code". Optionally you also can upload a build of the project (for example, web export ) so ppl can easily test the project without building it themselves.
5. Save and take a look at the game page if it's good.
6. Return to edit game page (using edit button at the top, or via your dashboard from the menu upper right).
7. Important! You need to set your game as Public to submit it in a jam!
8. Go to jam page and click submit project. Select your project and answer the questions if the jam host has put some.
If this is your first time participating a game jam on itch, I recommend trying steps 1-6 already today. You definitely shouldn't leave it to the last minute, as you cannot submit after the time is up. The eighth step can't be done until the jam has started.
Also note that itch has initial limit of 1 GB per upload (I believe they can lift it by asking), so be sure your project doesn't get too big - be vary of adding massive packages and assets.
Edit: Also, be warned: after tasting what is it like to participate in a game jam, there's no turning back! Have fun!