There are many ways of purchasing digital assets and crypto currencies.
Whilst coin purchases may be made directly in some cases via bank card, in the main purchases are made via an online exchange, of which there are many.
Much the same way that stocks and shares are purchased you register an account on an exchange, verify who you are with id and address information to satisfy money laundering regulations, transfer funds from your bank to the exchange and make the purchase.
Unlike buying shares, you are not buying a part of a company when you buy a crypto, and rather than trying to gauge a company's future income, you are anticipating change in the demand for a particular token or coin or you wish to use the asset to purchase a product or service.
If it looks as though the coin will be widely used, and therefore in demand, it's value should increase.
Each of the 1000 or more 'crypto currencies' represent particular systems with inherant methods, some far better than others.