Rebecca,
The Time Capsule icon will not stay on the desktop continuously. Normally, it appears when a backup starts and disappears when the backup is complete. This is normal.
Double click your hard drive icon in the upper right hand side of your computer. On the next window, look for your Time Capsule under the SHARED heading. Is it there?
If not, click anywhere in an open area on your desktop so the Finder menus appear at the top of your screen. Click on Finder, then on the General tab.
There is a heading that reads "Show these items on the Desktop"
Make sure there is a check mark in the box next to "Connected Servers."