There are numerous sites that allow you to buy and trade Bitcoins, please be aware of the "reserve" they list too, sometimes they will not have enough in reserve which can stall your transactions.
As a newbie, by all means don't do a private transaction with anyone in chat nor in the forums, there are a lot of scammers that pray on newbies. Stick to the official exchanges. There are sites such as www.bitcoinstore.com for which I have used to buy equipment for myself and other people and they're fairly quick.
It's one of those types of things that you need to use your common sense, if it seems to good to be true, it probably is. Watch out for other so called newbies looking to do transactions with you.
To prevent yourself from being a target by a scammer or other bad elements from here on out, don't call yourself a newbie, just ask the question.