Can I buy a US iPhone and use it in the UK?

Can I buy an iPhone 4 from the US, and put a UK sim card in it, and use it normally?
Does it have to be factory unlocked, or can I unlock it myself?
Also, will I be able to use 3g on it?

Most phones sold in the USA do not have removable sim cards

Yes you can. The cheapest iPhone to unlock is an AT&T iPhone. So if you can find one that has been previously activated at least once, you can get it factory unlocked cheap at places like iPhoneUnlockedCheap.com You can also unlock it yourself, however it will not be factory unlocked. You will have to jailbreak it which is risky and once you do, it will have problems with iOS updates.