URL Flipper was designed to be invoked by shortcut keys:
You can also access URL Flipper through the Firefox menu bar. It is located in the Go or History menu.
Let's say that you are at http://example.net/foo/42/bar3/. When you try to increment or decrement this URL, URL Flipper initially does not know what to do with this URL, so it will ask you to specify which part of the URL it should increment or decrement. It will look like this:
You will only see this dialog once! Now that URL Flipper knows how to handle URLs that look like this, the next time you try to increment or decrement a similar URL, URL Flipper will increment or decrement the URL using the information that you have already supplied, without displaying the dialog seen above!
If, however, you try to increment or decrement a different URL, then URL Flipper will show you the selection dialog again. For example, after specifying that you wanted to change the "42" in http://example.net/foo/42/bar3/, URL Flipper will not show you the dialog when you subsequently try to increment or decrement http://example.net/foo/47/bar3/, http://example.net/foo/65536/bar3/, etc. However, if you try to increment or decrement http://example.org/foobar?x=42, then URL Flipper will pop up the selection dialog because this is a new and different URL pattern.
If you want to force URL Flipper to show the selection dialog the next time you want increment or decrement a URL, you can use the Clear URLs option to force URL Flipper to forget all of the URL patterns that it has encountered so far. For example, after specifying that you want to change the "42" in http://example.net/foo/42/bar3/, you decide that you now want to change the "3" in "bar3" instead. Clearing the list of encountered URL patterns will force URL Flipper to show you the selection dialog so that you can select a different portion of the URL to change.
While the decimal, octal, and hexadecimal options are fairly self-explanatory, the general-purpose alphanumeric option may seem confusing to some.
Aside: The astute observer will note that the first two cases really are just sub-cases of the general third case. Indeed, URL Flipper makes no distinction between the three.