Hi
I'm not sure I understand what you are trying to achieve.
A text input box will save to a specified variable. This variable can be inserted into the URL box in a launch web page action by using /<variablename>. This can then launch the specific URL that the variable specifies, if it exists (if not, an error message will appear). I'm not sure this would get them to search results since I'm not sure where in terms of search results you want to take them. If you are tring to get them to a search engine and then have the search engine search the entered term, that one is beyond my skills.
If you could be more specific, perhaps include a basic sample .imp file, I and other Forum members may better be able to assist.
Kind Regards