If you are not using the Subscription form control which we distribute with Sitefinity you will have to use the Sitefinity API to create subscribers and assign them to newsletter. Bellow is a sample how you can add a subscriber to newsletter:
Telerik.Notifications.Newsletters.DataManager dm =
IGroup subsriberGroup = dm.GetGroup(groupId);
ISubscriber subscriber = dm.CreateSubscriber(userEmail);
IGroupSubscriber grSubs = dm.CreateGroupSubscriberRelation(subscriberGroup.GroupId, subscriber.SubscriberId);
the groupId variable is of type Guid and represents the ID of the subscriber group you want to assign the user to.
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