For some people this might be confusing, so the first thing you have to know is that you need to create a Developer account (free), at https://labs.aweber.com/. This account is not the same one as your AWeber account.
Don't worry, you don't need to be a developer to get this integration done. These steps should guide you through the integration process. And BTW, thanks to Angela for inspiring this help article!.
* Before you get begin, make sure you already have a working subscriber list in AWeber. The list name is going to be important during the implementation process.
Create your Developr account at https://labs.aweber.com/
Confirm the Verification link sent to your email and Log into your AWeber Labs Account
Click on the Create New App Button.
Fill in the information with your data. The name is of your choosing, the description is as well. The author is as well, and the URL should be from your website, but you could also add example.com for our purposes.
Once you create the new app you are almost done! Copy this information and keep it handy.
Now also copy and keep your specific AWeber subscriber list handy. *Make sure your list is active.
Log into your CotactUs Account, here http://www.ContactUs.com/login and click on the "Forms" button, located on the upper bar of your ContactUs admin panel.
Select the form you want to modify and click on the Submission Settings tab
Click on Software Integrations >> AWeber Integration.
Fill in the required information, use the API key and API secret from the ones you got at labs.aweber.com and your newsletter subscriber list *Located in your AWeber account.
*Make sure you turn on the "Enabled" switch.
Click on the AWeber Authorization button. This will open up a pop out window with the AWeber login form. Once you successfully verify the account hit SAVE.
A green border will appear in your AWeber badge in the software integration panel. Make sure you hit SAVE and PUBLISH at the bottom of the Form Configuration Tabs.
And... you are done! Just make confirm that your subscribers are in fact being delivered to your AWeber Subscriber List.