You are unable to delete a campaign, however you can archive an expired campaign.
Doing so keeps the campaign out of your everyday manage view but enables you to retain the campaign information should you need to duplicate it in the future, or call up reports for the campaign performance at a later date.
To archive a campaign, select "Expired Campaigns" and then click the archive icon at far right to archive the campaign.
If you've created a test campaign (for testing purposes) simply edit the end date of the campaign to a date/time that has passed. This will change the campaign status to "expired" at which point you can archive the campaign.