You can create a Facebook application from scratch, but it's easier to use a site such as Popfly. This allows you to create apps without coding. We're going to create an application that maps graphics on to a rotating sphere - either third-party graphics or users' own photos.
Popfly applications are called mashups. To make one, click the Create, Mashup link. This loads the Popfly developer, which has a series of building blocks (or code objects) that can be dragged on to the design surface. Each block can be modified to make it act as you wish, then linked to other blocks to build a complete application.
Drag the block you want to use into the design surface, then click the wrench next to it to modify its properties. This zooms into the block and lists elements that can be changed (types of images in this case). When you've finished making changes, click the wrench again to return to the main screen.
Next you need to set up a rotating sphere to display the images. Find the Photosphere block and drag this into the design surface so that it's displayed alongside your first block. Click once on the Live Image block and once on the Photosphere block to join them. Your basic application has now been created.
You can preview the application by clicking the link at the top of the design surface, and save it by clicking Save above this in the top panel. To view your project once it's been saved, click My, Projects. This will display any work you have on Popfly. Next we'll share the application so other Facebook users can access it.
After clicking the Share link, you'll see a screen where you can enter details about your project. There's also an option to provide a link to it on Facebook - under the heading Publish. Select this and click Post. Once you've logged into Facebook you'll see a link to the new application under your Profile.