ATOMs can be purchased by using base cryptocurrencies like BTC or ETH, through online exchanges such as:
Binance -- https://www.binance.com/en/trade/ATOM_BTC
Poloniex -- https://poloniex.com/exchange#btc_atom
A list of exchanges carrying ATOMs can be found at https://coinmarketcap.com/currencies/cosmos/#markets
In the next sections, we will go through a couple of ways to creating a Cosmos wallet, if you don't already have one:. These wallets will be yours to own, which you can use as, literally a wallet, to store your ATOM tokens, so you can then stake them to earn rewards.
Terminologies -- if you're a little confused between Cosmos and ATOM, here's a quick take on them:
Cosmos is a blockchain built on Tendermint powered by ATOM tokens
Tendermint is the underlying consensus protocol for Cosmos
ATOM is a fungible cryptocurrency used in the Cosmos Hub for transfer of value and as "gas" to pay for transactions in the Cosmos Hub
Cosmos Hub is the first implementation of Cosmos aimed at becoming the connector between blockchains, or in other words, "interoperable blockchain hub"