Probably the most comprehensive list of ways how to get bitcoins (exchanges, foundries, etc.) is here:

https://en.bitcoin.it/wiki/FAQ#How_can_I_get_bitcoins.3F

Any usually you will just buy them at an exchange:

https://en.bitcoin.it/wiki/Buying_bitcoins

I used MtGox so far and had no problems with it, except that the price there is usually higher than at other exchanges. For the exchanges, you usually have to register with some way of identification. This takes some time, days to 2 weeks.