How do I embed a membership application into my website?
Take a look at “Web Forms”:
https://help.infusionsoft.com/userguides/campaigns-and-broadcasts/campaign-goals/create-a-web-form
That will depend on your high level design. Are the members to be registered and maintain on your server or specifically using Infusionsoft as the data source? I would look at Memberium as it’s already designed around memberships with Infusionsoft specifically in mind.