If you know someone who holds some bitcoin, you can ask them directly if they might be willing to sell some of it to you. Please note that unless their primary business is to buy and sell bitcoin, they are likely to charge you a high price for their time and effort.
If you don't already know a seller personally, there are various exchange services that offer to connect Bitcoin buyers and sellers. When dealing with a new person, it is preferable to make only a small initial trade. You should not make large payments to another person until several small payments have been made without any problems.
Example of buying bitcoin on an exchange:
- Buying bitcoin on LocalBitcoins
Some exchange services also offer to store bitcoin for you. Please note that if you store your bitcoin with other people, you now hold human promises instead of mathematical / game-theoretic promises. There are some situations in which this is reasonable. The following page examines this issue in more detail:
Storing bitcoin with other people
You can also store bitcoin yourself. Please see the following page for more information:
How to store bitcoin