The best way would be to store the data collected in the form in a database and either: (A) encrypt the database data so that it's just garbage until you decrypt it or (😎 use an SSL connection and very very stringent access protocols so that only a select few users can get access to the data.
Either way, using SSL is a big plus. The encryption has it's down-sides; however, it does mean that even if someone broke the SSL encryption (unlikely, but still possible) that your data would still be "safe" as long as they didn't have the encryption key.