The “requesting a transaction” means you want to transfers some coins (let’s say bitcoin) to someone else. When you make the request the request is broadcasted to all the nodes. Then the nodes verify that (from all the history of transactions) you are not double spending your coins. When verified successfully the transaction is added in a block which is then mined by a miner. When the block is mined, your transaction is confirmed and the coins are transfered.
While it’s very easy to buy Bitcoins - there are numerous exchanges in existence that trade in BTC - other cryptocurrencies aren’t as easy to acquire. Although, this situation is slowly improving with major exchanges like Kraken, BitFinex, BitStamp and many others starting to sell Litecoin, Ethereum, Monero, Ripple and so on. There are also a few other different ways of being coin, for instance, you can trade face-to-face with a seller or use a Bitcoin ATM.
Bitcoin has been criticized for its use in illegal transactions, its high electricity consumption, price volatility, and thefts from exchanges. Some noted economists, including several Nobel laureates, have characterized it as a speculative bubble. Bitcoin has also been used as an investment, although several regulatory agencies have issued investor alerts about bitcoin.