I'm writing some code to learn more about the bitcoin processes. I've got most of everything figured out, but I'm wondering about base58 encoding. https://en.bitcoin.it/wiki/Base58Check_encoding
Let's say I have the following bitcoin address and private key (obviously I won't be using this one for anything important.)

Address: 1JHYG91McMgviqDDLSXq1TsPvZB7LYxV1s
PrivKey: 5JczEN6uCWESxHLyvnLbCWtjBJkTmHCtZBYcQztspvDJctmdKmF

If I use the chart on the base58 page linked above, then I convert each character of the private key into a number from 0 to 57. Do I use 6 bits to represent each number, and the concatenate the result?

If so, then , I end up with something like this:

Or in hex,

Since that doesnt really bear any resemblance to anything else I've encountered, I'm wondering - how exactly do I get a private key from the WIF and vice versa? Is there an easy "for dummies" link somewhere around from which I can get the rundown?

What I'd like to do ultimately is have a function that I can enter an arbitrary 256 bit number and then be able to transform it into the WIF, and take a WIF value and convert it back into the 256 bit number.

My mindset so far essentially goes like the following - Convert each character of the private key into a 6 bit number, concatenate each successive value into a single string.
I'm guessing this is the wrong approach, and would love a little bit of help (yeah, pun intended.)

I have a SHA256 library and everything else that's necessary pretty much ready to go, at this point I'm just stuck on base58. Thanks!