for links to the best btc exchanges go to the {bitcoins} little biggy.

what follows is how to buy from local bitcoins, the best option in my opinion.

the fastest way is bringing cash to a bank near you. localbitcoins.com is an escrow protected marketplace of individual traders that can get you coins this way today if you're willing to spend a little time navigating through their virtual bazaar, here's how.

1
register at https://localbitcoins.com/register/
^do not use a throw away email account since you need to monitor notices and respond quickly^
^you can skip 2 factor authorization for now if you use a strong password^

2
go to https://localbitcoins.com/instant-bitcoins/
enter your country, currency, and select a payment method that works for you eg bank transfer or paypal. note you can even pop into a local bank and deposit into your traders account if you'd rather use cash.

these methods are all safe if you have selected the right trader by:

a at least >50 trades and >98% feedback
b convenient payment method
c online now (green dot next to name)
d price (beware great prices)
e. doesn't need verification

3
perfection is rare, look at suitable traders and note their instructions, you will get the idea after reading a few.
go right ahead and make a trade request; your trader will give you specific instructions promptly, the competent ones are all about speed. if you don't get a prompt response cancel your trade in the "dashboard" and find someone else.

4
if the seller accepts your trade she puts her coins in escrow, they are released to you as soon as she says your payment was received. note seller's time zones to optimize speed for the entire transaction.

that's it. you're done, the coins are in your wallet (ie account) on the localbitocins site; you can send them anywhere on earth.

also note bitcoins are volatile and the exchange rate can change while you're doing all this, get 5% extra and you won't have to sweat it. you can use them next time or transfer them to secure storage later.