Abrabant, near the top right corner of the Greenfoot window where your game is, there should be a wide button that has a picture frame on it and says "share". Click the button. It should create a new pop-up window that has several options. One is to "Publish" which will upload your scenario. Click on it. Then enter a description, sign in, and then click the "share" button at the bottom of the window.
You can only upload scenarios that are less than 20MB.
Are you on a PC? If so, just go onto MyComputer, and browse around until you see the folder with your scenario in it. right click the folder, click properties, and it should have the size near the top of the properties window. The folder's size is always somewhat larger than the real scenario's size, but it gives you a good guess.
If you're on a Mac, I don't really know.
Unless you've got a lot of images, a lot of sounds, or really big images or really long sounds, your scenario should be well under the 20MB cap.