In Tezos there are two kinds of accounts: implicit (address starts with "TZ") and originated (starts with "KT"). You can only delegate from originated ("KT") accounts. Moreover, when delegating the entire balance of the account is used. One implicit account can only delegate to a single address.
So, to delegate you need to create a KT wallet and select a delegate for it. Please refer to the step-by-step guide with screenshots below.
Galleon is not an official Tezos wallet, but it's developed by the community of and supported by the Tezos Foundation. At the moment there are versions for Linux, Mac OS X and Windows. You can download it here.
Login into your Galleon wallet. Press "Add a Delegate" to create a new KT account (only KT accounts can be used for delegation).
Fill in the delegate address