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.
You can read more about TezBox here.
Create a new account (or log into your wallet) at tezbox.com. Press "Add Account" to create a new KT account (only KT accounts can be used for delegation).
Wait until the account has been processed by blockchain. This normally takes around 1-2 minute.
Click "Delegate", select "Custom" and enter delegate address. Press "Update Delegate" and wait until the operation has been added to blockchain (this normally takes around 1-2 minute).