Use Mapping tool on AcademixDirect Parter Poral to setup mappings for your form to AxD values.
Use your custom HTML-form and submit it to your own server. Names and values of the form needs to match exactly to what is specified in the Mappings Tool.
Set up your server (e.g. with PHP) for receiving your form, posting form data to AxD public API and fetching Session ID.
Use fetched ID for configuring results template.