Before buying a currency, you should create a wallet in which the purchased coins will be kept. Wallets are of several forms, but they all differ according to the kind of cryptocurrency you can keep in them. The wallets downloaded directly from the site of the currency are intended only for it.
For example, Bitcoin.org offers a large range of wallets for various devices (PCs, tablets, smartphones). They are available either in the form of downloadable software, or in the web version. Ethereium.org provides wallets for the Etherium, and so on.
However, there are also "multi"-wallets to keep several crypto-currencies. They are provided by third-party developers (for example, Cryptonator.com) or sites where a purchase will be made directly: exchanger-sites and online exchanges. The most authoritative ones among them now are: Cryptsy.com, Coinbase.com, AlfaCashier.com, and you can see a list of all online exchanges at BitMakler.com.
The algorithm for creating a wallet is simple: registration is conducted by e-mail, followed by verification - and the system sends a unique number.