Bitcoin itself can be anonymous but to buy them anonymously is challenging. You can cash pay some local merchant in your neighborhood to exclude your name from the great surveillance.
It is very dangerous to buy bitcoin face to face. If you decide to do so make sure you choose a very public place with lots of surveillance cameras otherwise there have been cases where the seller was robbed from the buyer.Same can happen if the seller is a dirty scammer. You can make bitcoin anonymous with a few tweaks but you have to search yourself for that. Localbitcoins remains a good place if you are really decided to buy or sell bitcoin face to face and know the risks of such trade.