If you have MOSS Enterprise and use browser-enabled forms, then you can easily provide a link that takes users straight into the new form itself. If not browser-enabled, there isn't really a direct URL to opening a new form. You can provide a link straight to the form template (.XSN), but what this does is give the user a prompt asking if they want to open template.xsn. They'd click "open," and then they'd be presented with the form to fill out that would have a submit button for submitting the data back to the SharePoint library or wherever else you want it to go.
Bear in mind that using rich client forms (not browser-enabled) will require all users to have whatever version of InfoPath you're building the templates with, or at least the form will have to be saved as whatever version your users have (IP 2007 can be made compatible with 2003, but not vice versa). Browser forms require nothing from the user really, but it requires MOSS Enterprise and the knowledge of how to make browser forms work well.
The other part about embedding the form in a web page can also be done, but that's more difficult. If you want to do that within SharePoint, then you can use the XMLFormView web part on a web part page. If you want to do it on some other website, then you'll have to be able to write an ASP.NET page that can embed it, but I don't know how to do that.