The Reusable Form web part will allow you to reuse a submission form across different web pages. To add one to your web page, you will need to be in edit mode, and then click the Add Web Part button at the top of the content area of the page.
After you click it you will be presented with the following menu
Select Cmich from the Categories section and Reusable form from the Parts section then click the Add button.
This will add the Reusable Form web part to the top of the content area of your web page. You will now need to configure the web part. Click the down arrow on the web part banner
Click Edit Web Part and the web part settings will open on the right side of the page
This is where you select the list where the submissions will be stored, to browse to the list, select browse site
Select your list in the menu and click ok
This will fill in the form address.
You can then customize the thank you message, the email address that will be notified by submissions to the form and the subject of that email.
You can reuse this form across sites by linking to the same form for submissions.