You need to:
1. add this to appsettings:
<appSettings>
<add key="ComponentArtSpellCheckDictionary/en-US" value="~/common/dict/us-english.txt"/>
<add key="ComponentArtSpellCheckCustomDictionaryManager" value="CacheCustomDictionaryManager"/>
</appSettings>
Hote the value for the dictionary key is a path to a dictionary file; you can change it, but this value must point to it's location.
2. add the httphandler. If you're using IIS 6: add
<add type="ComponentArt.Web.UI.SpellCheckCallbackHandler,ComponentArt.Web.UI" path="ComponentArtSpellCheckHandler.axd" verb="*"/>
to system.web.httpHandlers; if you're using IIS 7 add
<add name="ComponentArtSpellCheckHandler" type="ComponentArt.Web.UI.SpellCheckCallbackHandler,ComponentArt.Web.UI" path="ComponentArtSpellCheckHandler.axd" verb="*"/>
In the demos we just add both, and I'd recommend you do the same.
That should be it for web.config- let me know if you have any issues.