Typically cryptocurrencies are "stored" in wallets.
A wallet is a software program that is installed on a computer, tablet or smartphone and serves to see the balance, transactions, and obviously serves to send and receive cryptocurrencies. Really a cryptocurrency is not stored literally in a wallet as if it were a conventional purse, rather it allows us to manage our digital assets comfortably.
There are wallets that allow you to manage different cryptocurrencies, and others that can only be used to manage a single cryptocurrency.
The cryptocurrencies have two networks to operate: testnet and mainnet.
The testnet is a network for testing. To learn how to use cryptocurrencies without risk of losing money, since the cryptocurrencies that are transferred by the testnet have no economic value. You can not buy or sell them.
So how could I get cryptocurrency for testing?
In faucets like the ones you will find in this website, here you will get cryptocurrency easily to start testing. It is recommended to stat with NEM: it has an easy wallet and cheap (low fee) and fast transactions.
The mainnet is the main network where cryptocurrencies that have economic value are transferred. You can buy or sell cryptocurrency in exchanges.
There are wallets that need to download the entire blockchain before they can work, while others can be used once installed.
Below you will find several links to the testnet wallets that are used in the most important cryptocurrencies.
The easiest and fastest Ethereum wallet is Metamask.
It is an extension for the web browser. It does not require downloading the entire Ethereum blockchain.
It can work with the testnet network (ropsten, rinkeby, kovan) and with the mainnet network.
One of the most popular wallet for Bitcoin is Electrum, though we can use another ones like copay, or bitpay for testing.
These ones do not need to download the entire blockchain before they can work, so they are faster than the official wallet.
The most popular NEM wallet is nanoWallet. It has several features other than send and receive XEM. You can config it to use testnet or mainnet.
It does not require to download the entire blockchain to work.
You can use Shasta web to create an account and manage your assets.
There is a testnet web called Jungle where you can create and manage an account.
The easiest wallet is Stellar Laboratory that includes an account generator, a faucet and a block explorer.
The wallet is called Daedalus This version requires to download the entire blockchain, so it will take time before you can use it.
The wallet is called Trinity and to use with testnet you must setup the following node: https://testnet140.tangle.works/
Iota blockchain is very fast and feeless.
The Waves wallet is included in the Waves client. For testing you can use the web version. It includes a DEX (Decentralized Exchange) and token management.
The most popular wallet is Neon. You can also claim gas with this wallet. But you can use the official wallet here for testing.
The official Dash wallet is called Dashcore You must download the entire blockchain before you can use it. You can config it to use testnet or mainnet.
The official Litecoin wallet is called Litecoin core You must download the entire blockchain before you can use it. You can config it to use testnet or mainnet.
The official Monero wallet also can work in tesnet Monero github You must download the entire blockchain before you can use it. You can config it to use testnet (node: monero-testnet.exan.tech:28081) or mainnet.
The official Zcash also can work in testnet but there are other popular wallets that may work in testnet.
In official client you must download the entire blockchain before you can use it. You can config it to use testnet (add testnet=1 addnode=testnet.z.cash) or mainnet.