You can use the 366 Degrees Contact Create API to submit contacts to a 366 Degrees landing page. The landing page could be used to add contacts and subscribe them to a subscription list or it could be used as the entry point to a 366 Degrees Drip campaign.
The crucial part of this is process is that you must first have a landing page created in 366 Degrees and that page must be launched as a stand alone campaign or a Drip campaign. This way your external form will get some of the core functionality when submitting that comes with 366 Degrees (Auto-Responder email/Thank You email, adding to subscription list, adding to drip campaign).
Once your landing page is scheduled as part of a live campaign you will need to navigate in your browser to the live 366 Degrees Landing Page and view the source code. There are several values you will need to obtain to use the API to submit to the form.
Familiarize self with API
Create Landing Page in 366 Degrees and set submit actions
Schedule landing page as stand alone or first step of Drip
Navigate to LIVE landing page, view source
Find Submit hidden values (search source for Page_ID) you will need App_Key, App_Secret, Lead_Source, Subscription_Id, Page_Id.
PageType will be set to "landingpage" and the CampaignSchedule_Id value will be found in the url for the live landing page.
From this point you should have everything you need to utilize the 366 Degrees API to connect your external data capture to 366 Degrees.