It depends on the encryption mode you're using:
For CTR, CFB and OFB modes, the IV simply needs to be distinct for every ciphertext encrypted with the same key. (For CFB and OFB modes with less than full-block feedback, there are certain "weak IVs" that should also be avoided.)
For CBC mode, the IV needs to be unpredictable. One way to achieve that is to generate the IVs randomly, although other methods (such as encrypting a counter with the raw AES block cipher — preferably with a separate key, if there's any chance that an attacker might be able to control the counter — and using the result as the IV, or even, equivalently, using a fixed IV and prepending a unique nonce to the message) can also be used.
In any case, the IV does not need to be kept secret. If it had to be secret, it would be called a key instead.
Also note that none of the traditional encryption modes mentioned above are secure against chosen-ciphertext attacks (i.e. attacks where the attacker modifies the ciphertext, or makes up fake ciphertext out of whole cloth, and sends it to the recipient to see what happens). In particular, all of them (but especially CTR and OFB) are malleable, so that an attacker who can flip bits in the ciphertext may be able to flip corresponding bits in the plaintext. Unprotected CBC mode is also vulnerable to padding oracle attacks, unless special care is taken to prevent them (and, even then, it still remains somewhat malleable).
To protect your messages from modification and to avoid such chosen-ciphertext attacks, you'll need to either use an authenticated encryption mode, or compute a message authentication code (such as HMAC) on the ciphertext (and IV!) after encryption (and verify it before decryption).