Creating An Account In Ethereum Wallet
Start up Ethereum Wallet. Make sure that you are on testnet by selecting the menu Develop -> Network -> Testnet(Morden).
On the main page, click on Add Account, and enter your password (and remember it).
Getting Some Coins On Testnet
To get some coins to test with on testnet (from Morden),
One way to get Ether is by using the Ethereum wei faucet. Just type in your account address and enjoy some free ether.
Note that the site linked to above was not working @ 01/05/2016.
You can also get some ethers from morden.ether.camp or test.ether.camp by clicking on the [Get Free Ethers] button on the top left of the page.
Note that these sites were not working @ 01/05/2016.
Deploy A Contract
Please refer to The Ethereum Wallet: An Introduction for Non-Devs for a guide to deploying a contract on testnet.
There are not too many active peers on the Testnet network. Synchronising your blockchain is going to take a while, with periods when no synchronising occurs as connections to the few peers drop off with the following message:
I0501 19:08:26.403691 25657 downloader.go:267] Synchronisation failed: no peers to keep download active
Just be patient. And just shutdown and restart repeatedly to speed up this process.