why can the U.S. enforce their laws in other countries?

It can't. What makes you think it can?

Each country is sovereign and whatever laws the US likes to think it makes that apply elsewhere, it cannot enforce anything outside its own borders. If the US tried that, it would not go down well in the other country, and there would be huge diplomatic problems. US officials do not have the power of arrest outside the US, and if they purport to arrest someone in a foreign country, then unless the people who do it are accredited diplomats and therefore protected by diplomatic immunity, they could be arrested themselves for false imprisonment. If they have diplomatic immunity, they would no doubt be expelled from the country for "activities incompatible with their status".

Ah, yes, diplomacy... there is the convention that the ambassador in another country and his or her staff are accredited by that country to be there, and they are immune from the law. It all helps oil the wheels.

Let's say you work for the US Department of State and you get posted to the US Embassy in Saudi Arabia. You have the day off and it's hot, hot, hot... Riyadh is basically in the middle of a desert... wouldn't you just love a cold beer? It would taste so good! Your problem is that Saudi Arabia runs strictly according to Islamic law so you can't. All alcohol is illegal, and possessing any is punishable by flogging. In public. BUT because you're an accredited diplomat, and the Saudis let the embassy diplomatically import what it likes, you can have an imported beer. Of course you would drink it inside the embassy compound or your house so you don't cause a public scandal, and your diplomatic immunity prevents you from ending up in a Saudi court for it. The most they can do if they don't like you is withdraw accreditation and kick you back to the US.

I remember expulsions during the Cold War. Soviet diplomats would turn out to be KGB spies, but because they were accredited diplomats, the most the country they were in could do was send them back to Moscow.

If this person returns to the US, THEN they could be arrested.

Other answers have mentioned extradition. This is ONLY for crimes committed in the US, where the person has left the US and the US wants to bring them back for trial. Obviously that's a reasonable thing to ask. But it is not an easy process, and involves diplomatic negotiation between the US and the other country. Fleeing to Europe is usually quite effective, because European countries are not entirely convinced (the diplomatic way of saying they aren't convinced) that the USA is as good as they are at offering a fair trial. Extraditing alleged murderers is especially difficult as European countries don't use the death penalty. You might have noticed that the US can't do anything about Ed Snowden, because he's in Europe and therefore outside anything US authorities can do.

One thing that could happen is if the other country asks US police to help. No problem there, because then they are operating with permission and under the authority of the other country's police.

A nice example of trying to enforce the law in other countries is FATCA (the Foreign Accounts Tax Compliance Act). This requires all banks, worldwide, to report details of accounts owned by US citizens. The intention is to prevent tax avoidance by stashing your money outside the US. Of course this cannot be enforced outside the US, but what the US CAN do is make life difficult for big international banks that operate in the US. The general response by non-US banks to this has been, at least I know this is true in the UK (I'm British), to refuse to allow Americans to have an account. 'Cos then they don't have to report!

And this is why US citizens who have moved to another country are increasingly renouncing US citizenship. Once they've been abroad long enough to get citizenship where they live now, they renounce US citizenship and then they have a free choice of local banks to put their money in. AND they don't have to file taxes with the IRS any more. Of course the US government has noticed and that's why it now charges $2.350 to give up being American.

One last thought on diplomacy. Diplomats never say no. The polite way to say it is "we will make every effort, but it may not be possible".

The person's act would have to have some effect on the U.S. or its citizens or its inhabitants.

So Osama bin Laden murdered 3000 people in the U.S. It doesn't matter whether it was legal in Afghanistan for him to do that: he murdered people in America, and that violates U.S. law.

Their country, their rules.

If they want people to drive on the left side of the street, then its OK for americans to drive on the left side of the road when they are in that country.

Similarly, if Spain wants to allow its people to drink absinth, then its not for the US to arrest absinth drinkers (if they do their drinking in Spain.)

By the same principle, if England forbids people from having a gun is illegal, they can't come and arrest people in the US who have a gun. Even British citizens.

What is legal or illegal depends more on where you are than what country you are a citizen of.

They can't. US laws and the US constitution mean absolutely nothing outside the USA. If someone commits murder in the USA and escapes to Europe or Canada, that person will not be extradited to the USA if they face the death penalty.

ICE can. If it is child porn or slavery, human trafficking. They would need to extradite you. If both Countries have signed the U.N. agreement. That is easy to do. You can also be charged in both Countries & be sent to prison in both for such. So 20 years here, 30 years there. It can add up.

Extradition treaty. Usually the crime in question is somehow related to the United States hence the grounds for invoking the treaty rights.

They can't actually. Not sure why you think they can. They can arrest someone from another country for committing a crime IN the US, but they cannot go to another country and arrest people. They cannot arrest people in another country for what they do in the other country.

Giving an example of what you are talking about would make answering this vague question a great deal easier.

They only can if they have an Extradition Treaty with the other country.

They can't and don't.

This is not a question of extradition you IDIOTS.

Extradition is only for crimes committed IN the US, and the person that committed the crime fled FROM the US.