The simplest of these is the electronic codebook (ECB) mode, in which the message is split into blocks and each is encrypted separately. The disadvantage of this method is that identical plaintext blocks are encrypted to identical ciphertext blocks; it does not hide data patterns. The advantage is that error propagation is limited to a single block.
In the cipher-block chaining (CBC) mode, each block of plaintext is XORed with the previous ciphertext block before being encrypted. This way, each ciphertext block is dependent on all plaintext blocks up to that point. On the other hand, an error in one ciphertext blocks impacts two plaintext blocks upon decryption.
The cipher feedback (CFB) and output feedback (OFB) modes make the block cipher into a stream cipher: they generate keystream blocks, which are then XORed with the plaintext blocks to get the ciphertext.
With cipher feedback a keystream block is computed by encrypting the previous ciphertext block.
Output feedback generates the next keystream block by encrypting the last one.
A more recent mode is counter (CTR) mode. CTR isn't an acronym; it is given a three letter name just to be like the others! Counter mode also turns a block cipher into a stream cipher. It generates the next keystream block by encrypting successive values of a "counter". The counter can be any simple function which produces a sequence which is guaranteed not to repeat for a long time, although an actual counter is the simplest and most popular. CTR mode has very similar characteristics to OFB, but also allows a random access property for decryption.
All modes (except ECB) require an initialization vector, or IV - a sort of dummy block to kick off the process for the first real block, and also provide some randomisation for the process. There is no need for the IV to be secret, but it is important that it is never reused with the same key. For CBC and CFB, reusing an IV leaks some information. For OFB and CTR, reusing an IV completely destroys security.
Because a block cipher works on units of a fixed size, but messages come in a variety of lengths, it will also be necessary to pad the final block. Several padding schemes exist. A very simple one (really only suitable when the plaintext will be treated as C style stringss) is to simply pad with null bytes. A bit more complex is the original DES method, which is to add a single one bit, followed by enough zero bits to fill out the block (if the message ended on a block boundary, a whole padding block will be added). Most complex of all is ciphertext stealing, which avoids further message expansion.