For the visually-oriented, the process is explained here: http://counterparty.io/get-started/. If you prefer to read, keep going.
Counterwallet can run on mainnet (the "real" Counterparty network) and on testnet (a test Counterparty network).
Use Counterparty on Main Net
Mainnet uses "real" virtual tokens and assets.
To get started, visit https://counterwallet.io and click on Create New Wallet.
Back-up Your Wallet's Pass phrase
Please note that Counterwallet or the Counterparty Project have no way to access your wallet, any of the addresses or know your pass phrase.
It is therefore very important to memorize or write down your pass phrase (or password, in case you use Quick Access URL) on paper or some other medium which can serve as backup should you forget your pass phrase.
On computer, never store your pass phrase / password in plain text so that it can become easily accessible to hackers or trojans (for example, to save it on your notebook as "counterwallet_wallet.txt" would definitively not be a good idea).
NOTE: Counterwallet does not require any account number of wallet ID. All that you (or any other person) need to access your wallet is the wallet pass phrase.
Get Tokens or Assets
In order to be able to send or buy tokens or assets, you first need to have some sent to you (to one of addresses in your wallet). Most users start with a small amount of bitcoin (e.g. 0.01) sent to the first address in your wallet, although any Counterparty address in your wallet can receive bitcoins, XCP and any asset/coin that was issued on top of Counterparty.
If you are new to Web wallets or cryptocurrencies, spend some time using Counterparty on testnet and when you use Counterwallet on mainnet, start with very small amounts.
Try Counterwallet on Counterparty Testnet
The Counterparty test net (or testnet) uses "fake" virtual tokens and assets. The Counterparty testnet runs on Bitcoin testnet, which is an alternative Bitcoin blockchain, to be used for testing.
The bottom line is, it works the same way as Counterwallet on mainnet, but it gives you a way to risk-free try all Counterparty features.
When you log on, you will find instructions on how to obtain a testnet version of XCP tokens. You can also use a Bitcoin testnet faucet to get "test bitcoins" for testnet. You would send them to an address in your Counterwallet account on Testnet.
To access Counterwallet on testnet, please visit here: