Several options:

1. Connect to the bitcoin network directly, parse all messages, verify the blocks and insert all the transactions contained within it into the MySQL db. This is going to be a bit hard since you have to write code to connect to the network.

2. Run bitcoind side-by-side with the MySQL db and use some combination of the getblockcount, getblockhash, getblock, gettransaction RPC commands and insert the transaction data into the MySQL db. You can run a cron on this every 5 minutes or so and you should have a fairly up-to-date MySQL db. This comes at the cost of considerable disk space since you'll need to have the entire blockchain for bitcoind (30 gigs and growing).

3. Connect to some other service and get the data that way. Blockchain.info is the obvious one and they have a wonderful API for getting all the new data you need. Unfortunately, you'll have to trust them to provide the right data. There's also electrum servers which provide data using stratum and ABE and some others. Heck, if you can get someone to open up their RPC port (8333) on bitcoind, you can connect to their bitcoind and use the same commands as #2. The drawback here is that you have to trust a third party in some way, shape or form, though, of course, you can write your own verification code.

Regardless of which thing you choose, you'll need to handle some difficult things like orphaned blocks when trying to keep this db up-to-date.