Stuck trying to get my greeter contract onto my test blockchain

Hi,
I am a total Noob here, so apologies in advance :-)

I successfully followed instructions here to create my private testnet https://souptacular.gitbooks.io/ethereum-tutorials-and-tips-by-hudson/content/private-chain.html

I created a user and followed these steps to succesfully "mine" some ether for it https://www.ethereum.org/ether

I then followed these instructions to create a "hello world" contract https://www.ethereum.org/greeter

I got up to compiling it and getting it ready for deployment.

I started the miner and I can see that the transaction is there ready to be mined:

I1220 12:03:18.115644 4624 miner.go:119] Starting mining operation (CPU=2 TOT=4)
I1220 12:03:18.117937 4624 worker.go:570] commit new work on block 480 with 2 txs & 0 uncles. Took 2.2176ms

And yet, nothing happens!

I am not sure what step I am missing. Can anyone advise?

Many thanks.

Daniel