I feel like a bit of an idiot asking this, but is there a general rule of thumb on how to dial from a foreign cell phone when traveling internationally? Or does it vary by country?

As an example, I'm from the US and have a US-based cell phone.

I truly can't recall the last time I made a phone call while out of the country even though I travel internationally a half dozen times a year.

I usually program into my contacts the local US consulates/embassies but am curious if I'm entering the number correctly.

As an example, if I'm in London, do I dial the number for the US embassy in the same fashion as if I were dialing from a landline in London? Or, the same as if I had a UK-based cellphone? Or as if I'm dialing from the US?

I usually program in the "+" and country code. However, sometimes the dialing guides say that you don't need an extra "0" or some other such number if dialing from within the country.

All of this confuses me greatly and I'd like to know before I ever actually have to make an urgent call.