All users in your Salesforce org are related to one profile. Profiles are then given access to RecordTypes, thereby giving them access to different types of records within a given object. In this case, if you want to allow a certain profile to have access to a Soapbox Mailer Campaign (and Campaign Member) record(s), follow these instructions.
1) Login to Salesforce, and go to Setup > Administer > Manage Users
2) Click on the Profile you'd like to have access to the Soapbox Mailer RecordType
3) On the Profile page, under the Apps section, click the "Object Settings" link
4) On the Objects Settings page, click on the "Campaigns" link
5) On the Campaigns Objects Settings page, click on the Edit button
6) On the editable version of the Campaigns Objects Settings page, under the Campaign: Record Types and Page Layout Assignments section, check the box in the row for Soapbox Mailer under the column "Assigned Record Types".
7) Click the Save button
8) Do the same for the Campaign Member object
That's it! Now this Profile has access to Soapbox Mailer Campaign and Campaign Member RecordTypes.