What is the approach to calculate an Ethereum address from a 256 bit private key? For a given private key generated by MyEtherWallet, I would like to see I have the tools to independently arrive at similar results. 

Wrote a wrapper around Keccak to accept both hexadecimal and ASCII inputs to be sha3-224 or sha3-256 or  sha3-384 or sha3-512 hashed. Hashes are consistent with Test Vectors. Would like to apply it with bitcoin-explorer (bx) version3 commands to see if I can synthesize ETH addresses. If successful at synthesizing addresses for ETH, XMR, and MAX altcoins, I go through the effort of submitting a pull request to add sha3 hashing capabilities to bx version3, and update this Wiki concerning the application of bx to altcoins.
Start with the public key bytes (a bytestring of length 64)
Of that public key, take the Keccak-256 hash used ubiquitously by Ethereum (make sure you get that right, as the ultimately standardized SHA3-256 hash differs). You should now have a bytestring of length 32.
Drop the first 12 bytes. You should now have a bytestring of length 20, the Ethereum address associated with your public key.


Update: Oops! I see you want it from the private key, not the public key. That's harder. You have to first derive the public key from the private key, which is best with the help of an EC crypto library. I can show you some example code in Scala, but the EC math is mostly a black box to me. First, interpret the 256 bit private key as an unsigned big integer. Then, see e.g. here. Curve represents the named eliptic curve secp256k1. The details of the math are, alas, beyond me, but hopefully in whatever environment you are coding you have access to a high quality crypto library.

Update 2: In the comment thread, I speculated about where Ethereum's hash function diverged from the SHA3 standard. My speculation was mistaken, the version I thought was the incompatible change is the version Ethereum in fact uses. Thanks to work by Eric McCarthy, who chased this down in great detail. Please see this comment below for more details.