Confidentiality means keeping the information secret, or in other words preventing the unauthorised disclosure. Confidentiality can be obtained by using access control (using authentication to limit the access to information), or physical security (keeping your important documents in a locker), or by using encryption (only people who have access to decryption key can decrypt to read the information), or in some more similar ways.
Integrity means keeping information intact, or in other words preventing the unauthorised modifications. Integrity can be obtained by using access control (using authentication to limit the write access to information), or physical security (e.g. some banks apply a transparent film on sensitive areas of banker's cheques to avoid direct manipulations), or by using hash functions (however hash can just detect alterations but cannot prevent it to occur).
Authenticity means knowing the source of the information. If you receive a email from a regular customer to ship 1000 items at some address, and that regular customer generally settle all payments on monthly basis. Will you ship believing that mail was sent by that customer or will you try to verify whether actually it was sent by him only. But how you will verify? Do your mailing system has such function to guarantee the authenticity of mail message. Yes it has a feature called Digital Signature which can be used to validate authenticity [to know about how Digital Signature works click on the related posts from list on right side]
Availability ensures that the information should always be available but to authorised users only, so it can be further divided in two sections:
a. Keeping information always available: e.g. using backup / mirrored drives or RAID / server cluster / etc
b. Keeping it available to authorised users only: e.g. using authentication to keep unauthorised users out / using firewall to make available only few desired services / etc.
5. Non-Repudiation / Accountability:
Ensures that you are able to held people responsible for their actions. Usual practices are maintaining user access logs, using digital signature, etc.