You need to upload demos to some place that you can link to. Browse the music offerings here to get an idea of where to host. (If all else fails, use YouTube).
Once you have samples or demos that people can listen to, you can upload your music as a zip file and follow the instructions on the itch.io page to place it for sale (set a price for it.)
You can offer your music in exchange for a cover illustration or simply ask. Many artists offer their services for free - here.
However, a cover illustration is not that important for music - what is important is that there are demos that people can listen to (the first few seconds or similar songs - but with a beep or sound placed strategically so that people cannot steal it.
For games, it is important that the music loops and that you provide info on the length of the tracks and the type - .wav / .ogg / .mp3 etc.
There are so many music offerings here - really great stuff and many free ones - just browse the site and check what others did - then do the same.