You have multiple approaches for this, I believe. This isn't something I can help you with much, but if you post a description of how you need to export your data (IWP, CWP, PDF, xml, HTML...?), perhaps another forum participant can chime in with the help you need.
Not sure what you mean by "export to my web". You can export records as HTML table - this will produce a very basic HTML document. A more sophisticated approach is to export as XML, using a XSL styleheet - you can find some examples of this in the Examples folder that came with the application.
Either way, the result will be a HTML document exported locally - you will need to move it to your web site yourself, or use a FTP plugin.
Another option: if your site is built using PHP/MySQL, I believe you can update the remote MySQL database directly from Filemaker.