If you have any Bitcoin ATM in your area, give it a try (but be prepared to pay some rather high fees, that's the price of anonymity)

I always find handy the chipchap service in my country which allows me to buy bitcoins using fiat money via the bank's easy pay machine. Of course the fees are rather high, too, but it works like charm.

A lot of people will also suggest you the Localbitcoins, which is the best solution (that's what i hear, never used this service before).

But then again, all depends on what country you are in.