I'm currently coding a small Monero tool just to better understand how it all works. I already implemented address-generation from scratch (thanks to luigis address test page) and the next step is to scan the whole Blockchain for transactions that have outputs associated with an address. I have found the site xmrchain which lets you do just that for single transactions, like this random one: https://xmrchain.net/tx/a8fdf7a2fb4f153980f7b5b968f54bde375b0484fd897a2f9fb3139a9fe91c46 There, you can click on "decode outputs", supply your private viewkey and address, and it shows you which outputs belong to you.
Unfortunately, all these calculations are done on the server. Could someone explain to me how I would do the same thing manually, with my private/public viewkey, address, and all the transaction data you get with the /gettransactions RPC-call?