This is the first and most common question. For US Citizens the most popular is Coinbase(click here). This functions similarly to Paypal as you can link your bank account and/or credit card to purchase and convert back to USD.
There are several options on how and where to store your Bitcoin. Some wallets will allow you to transfer your Bitcoin into the currency of your country via a bank transfer or an attached VISA debit card. There are both online wallets and hardware wallets for safer storage.
Bitcoin mining serves to both add transactions to the block chain and to release new Bitcoin. The mining process involves compiling recent transactions into blocks and trying to solve a computationally difficult puzzle. The first participant who solves the puzzle gets to place the next block on the block chain and claim the rewards. The rewards incentivize mining and include both the transaction fees (paid to the miner in the form of Bitcoin) as well as the newly released Bitcoin. The blocks will get harder to mine depending on how many computing systems are mining the bitcoin. The more miners the more difficult the bitcoin is to mine. If computing systems are taken off the market the mining difficulties get easier. Watch an explainer animation(link)
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