I imagine that you are referring to Hive Web Wallet (hive-js), that is a lite (web) wallet, and it doesn't do SPV like the OSX one does (via BitcoinKit).
To build a lite wallet (web wallet in ethereum terms) I suggest to start with eth-lightwallet to create a web wallet to create keys and sign transactions that connects to a public ethereum node or a node you are hosting yourself (with geth for example), and the node doesn't have accounts or funds you use in the web wallet app, it just relays transactions to it.
You will also need the hooked-web3-provider or a similar solution to relay transaction you signed with eth-lightwallet to the ethereum node. Also to strenghten the solution you could connect to multiple servers so if one goes down your wallet still works, it's still not as strong as SPV but as there are no SPV JS solution yet for ethereum, that may be a good solution.
See the full example on eth-lightwallet repo
To run it, clone/download the repo, run npm install, drop the html file from the examples dir in your browser and it should work by default. I tried it with the geth host it connects to by default (22.214.171.124) and it works, if it doesn't, replace it with a public host or your own geth address (probably localhost).