1. Find and click the symbol icon on the window that appears.
2. Make up a name for the symbol (example: ADC0808) in the window that appears. Click OK. Then YES, if asked.
3. Draw out the part using lines, circles, rectangles, etc...
4. Place pin locations using the pin icon (below the drawing icons on the sidebar)
5. Place text for >NAME, >VALUE (make sure to change their layers to "name" and "value" also). Save progress.

6. Click the package icon at the top
7. Choose a name for the package (example: DIL28)
8. Draw the footprint you want (>NAME, >VALUE)
9. Place and edit pins (make sure number of pins matches your previous drawing). Save progress.

10. Click the Device icon at the top
11. Select the device name you came up with in step 2.
12. Click the add icon on the sidebar
13. Drop your symbol onto the workspace.
14. Click the NEW button in the bottom right.
15. Select the package name you came up with in step 7. Click OK.
16. Click the Connect button (next to the "NEW" button from step 13)
17. In the window that appears, match the symbol's pins to your package's pins with the long "connect" button. Click okay when done.
18. You're done. Save everything and now you can use that custom part in any project.

...Maybe my list is missing some minor stuff, so I really recommend doing it by the tutorial. If time is critical or a custom part just seems like overkill, just download the ic-package.lbr file from EAGLE.