Thanks for trying, but I see nothing on any of those pages that answers my question. The first one doesn't seem to have anything to do with Dark Wallet.
Darkwallet uses and is dependent upon an independent implementation(not Bitcoin Core) which interacts with the Bitcoin blockchain :
https://github.com/libbitcoin/libbitcoin-explorer (formerly sx)
https://github.com/libbitcoin/libbitcoin-server (formerly Obelisk)
That is why the first link is relevant.
How do these work together, exactly? How do these pieces interact with the Bitcoin network?
Need to read the content I linked to, to answer this.
What does the browser plug-in do?
The browser extension is a full wallet that focuses on privacy incorporating tools like coinjoin and stealth addresses
What does Obelisk do?
Now called libbitcoin-server acts as the Full node which communicates with the blockchain and other nodes because darkwallet is a thin client.
What other components are necessary?
Download and install the darkwallet extension in chrome or chromium:
https://www.darkwallet.is/Download ZIP.
Unpack the ZIP file.
Navigate to "chrome://extensions" in your browser.
Enable Developer Mode.
Click "Load unpacked extension" and select the unzipped folder.
DarkWallet is installed!
Than select a server:
https://wiki.unsystem.net/en/index.php/Obelisk/Servers