There is no need to uninstall Internet Explorer after installing Firefox. In fact, Windows and some programs need Internet Explorer to work properly. You may also need Internet Explorer to access certain sites, like Windows Update.
To make Firefox the browser that other programs open, see Make Firefox your default browser.
To remove Internet Explorer shortcuts, you can use the Windows feature Set Program Access and Defaults. See these articles on Microsoft's site for more information:
Based on information from Internet Explorer (mozillaZine KB)