New bitcoin are released during the mining process, in which network participants compete to record recent transactions with the winner receiving some previously-unreleased bitcoin as a reward. Those bitcoin then circulate when miners sell or transact these bitcoin.
Though it was once relatively simple to mine bitcoin yourself, the bitcoin mining industry has become so specialized and competitive that it is highly unlikely that an individual will successfully earn a bitcoin subsidy with their personal computers (individuals can however participate in mining pools to have a better shot at bitcoin subsidies).
Most individuals that are looking to acquire some bitcoin do so through online exchanges, which sell BTC in exchange for fiat currency or other cryptocurrencies (they also collect fees and generally require the verification of personal information). Many others, including a range of individuals and merchants, get bitcoin by accepting it for goods and services.