You can share your apps by downloading the source code as a .zip file and then sending that file to another person who will in turn upload the .zip file to their projects in App Inventor. In the Designer window, click "My Projects" in the upper left. Select the checkbox next to the app you want to share. Click the "More Actions" button and select "Download Source". A .zip file will be saved in your Downloads folder.
Notes: 1 - Some browsers will automatically unzip the file. The file needs to stay zipped. You may need to rezip the file, or alter your web browser's settings to prevent it from unzipping downloads. 2 - App Inventor will reject any file names with parentheses or spaces, so if your browser names the file something that has anything other than letters, numbers and underscores, you should change the name of the file before sharing it. App Inventor file names must begin with a letter and may only contain letters, numbers, and underscores.
To upload a .zip file as a new App Inventor project, go to "My Projects" and click "More Actions" --> "Upload Source". Select the .zip file from your hard drive and App Inventor will unzip it for you and display the project in your projects list.