how can I unlock my iPhone 3G to use it in Vietnam and Thailand?

You will need to contact your carrier. Only your carrier can unlock your iPhone spending on their unlocking policy. Which country are you in and what network are you on?

If it's locked to a USA carrier, it cannot be unlocked. No USA carriers will unlock an iPhone.

I'm afraid carriers in the US do not authorise unlocking.

I do not know how in Thailand, but in Vietnam you can use sim transplant, there is a solution for your iPhone 3G