The most complete method is to upload the manifest file to your server and validate it by URI. This will also check the availability of all resources listed in your manifest – if even one of them fails to download properly, the entire process of caching your offline web application will fail.
To learn more about offline web applications and cache manifest files, check the following resources:
TweetThis validation service can also be used by external tools. Either provide an URI to your manifest or the file's content as a string (GET and POST are supported for calling). The API either returns a JSON string or a JavaScript function for JSONP, when you provide the optional callback parameter.
Read the Cache Manifest Validator API documentation on GitHub.
The validator is now also available as an extension for Google Chrome, you can grab the source code here.
I've also created a TextMate bundle with a default manifest template and a connection to this validation service. It is available at GitHub and can also be downloaded directly.