At this time, HubSpot Sales does not offer embeddable forms for collecting contacts on your site.
With HubSpot Marketing Free, you can use lead flows and collected forms to capture contacts. With a Marketing Basic, Professional, or Enterprise account, you can use the forms tool to create HubSpot forms and include them on your pages.
Alternatively, with the help of a website developer, you can send contacts from your own forms to the CRM using the Contacts API. Learn more here.