That link is about creating a Bitcoin address from a key pair, not from the "wallet import/export format" which is said to "include built-in error checking codes" (from the "Private key" wiki entry).
Steps 4 to 9 describe how to do Base58Check encoding (but remember what I said about step 9). A WIF (wallet import format) key is simply a Base58Check encoded private key.
EDIT: so let me make this clearer:
1) Attach '80' to start of private key.
2) Perform SHA-256 hash on the whole string.
3) Perform SHA-256 hash on the result of the previous SHA-256 hash.
4) Take the first 4 bytes of the last SHA-256 hash. This is the checksum.
5) Add the 4 checksum bytes from point 4 to the end of the string from point 1.
6) Convert the result from a byte string into a base58 string.
EDIT: If you look here
you'll see the process (Base58Check encoding) described in a few steps:
A Base58Check string is created from a version/application byte and payload as follows.
1. Take the version/application byte and payload bytes, and concatenate them together (bytewise).
2. Take the first four bytes of SHA256(SHA256(results of step 1))
3. Concatenate the results of step 1 and the results of step 2 together (bytewise).
4. Treating the results of step 3 - a series of bytes - as a single big-endian bignumber, convert to base-58 using normal mathematical steps (bignumber division) and the base-58 alphabet described below. The result should be normalized to not have any leading base-58 zeroes (character '1').