Install the Arionum LightWallet, (found here), navigate to the integrated "Miner" tab, type "http://aro.hashe.rs" in the Pool field and click "Start Mining". That's it, you are now mining on our pool!
If you are a power user and you would like to get maximum mining performance, you should use Dan's Java Miner which is available here.
Under linux and mac, we recommend using Dan's Java Miner, which is available here.
A full guide can be found on the above url.
Arionum is one of the few coins that can be feasibly mined with cloud resources, for the time being. If you would like to give cloud mining a try, check out OvErLoDe's Cloud Mining Guide, which can be found here, on the Arionum forums.