how would i do this?

I would submit a form on your page to the destination of the other site's form. Look at the HTML of the other site and figure out:

- The destination of the form in question (the value of the form tag's action attribute) and,
- The names of the form's elements

Then create a form on your page that submits elements with the same names to the same destination. If you don't want the user to fill out the form, you can use hidden fields.