In my experience the most common way Americans express the need to use toilet facilities is to say, “I have to go to the bathroom.” Sure, there are others - “I have to pee”, “I have to take a dump” - but “go to the bathroom” seems to be the most common.
What is most common in other cultures, both English-speaking and other languages? We didn’t cover it in high-school German, but I doubt “Ich muss zum Badezimmer gehen” is what they say in Deutschland.
Most Asian cultures do not announce where they are going, when going to relieve themselves.
They say, “Excuse me for a moment.”, if they say anything at all.
In Australia, it’s far more common to say, “I have to go to the toilet.” Aussies don’t use the term “bathroom” or “washroom” much when they’re actually talking about the toilet.
You also sometimes hear euphemisms like “I have to use the facilities,” or “I have to go to the loo” (very English in origin) or “I have to see a man about a dog.”
If you’re just talking about announcements, I don’t think most Americans do that either. But what about, for example, if you’re riding in a car on the highway and you need to ask the driver to look for a place to stop?
Anything from “I must go powder my nose” to “I need a slash”, depending on company.
Do Aussies go to “spend a penny” as older Brits might say?
I have heard Nigerian tourists ask in English: excuse me,“where can I ease myself?”.
We should all adopt that phrase…I think it sounds kinda classy. 
Swedish: Jag måste gå på toaletten.
Icelandic: Ég þarf að fara á klósettið.
(Both litterally translate into: I have to go to the toilet)
No, we abolished the penny about 50 years ago. I’d just say “I’m going to the toilet” or “I’m going to the loo.”
When I lived in the US, I hated talking about going to the “bathroom” or “rest room”, because I didn’t want to bathe or rest. If I had to, I’d say, “Where’s the men’s room?”
Posso andare al gabinetto? (please can I go to the toilet)
The very first lesson we covered in my Italian class, well over a decade ago.
[QUOTE=Giles;1927972) I’d just say “I’m going to the toilet” or “I’m going to the loo.”
When I lived in the US, I hated talking about going to the “bathroom” or “rest room”, because I didn’t want to bathe or rest. If I had to, I’d say, “Where’s the men’s room?”[/QUOTE]
Foreign folks often say they don’t like saying “bathroom” or “restroom” because it’s imprecise. But to American ears the word “toilet” just sounds crude. It sort of sounds like saying “I need that thing that people piss and shit in.” Who says Americans have no subtlety.
je dois faire pipi…
Klingon: I have to drop Kirk and McCoy off at the pool.
For Spanish: "Casa de pepé. Donde esta casa de pepé?
Well, that’s what Steve Martin told us to say.
When I visited southern rural Mississippi about 20 years ago, I heard the term “I have to use the commode”.
Which made me giggle. To a nursing student’s ear the commode is the toilet seat with a bucket portable device that is brought bedside for patients with mobility issues. usually it was the job of the nursing student to clean and empty it.
Canadians are likely to use the term “Washroom”. And you had better wash your hands at minimum after you “ease yourself”.
Ah don’t get me started. I have been off work too long, I have been missing the daily discussions of elmination. The who what when where how and how mcuh of it all.
ASL uses the sign for"toilet" . Asking a child if they need to go is covered on the same page - i would use the expressions, or similar, or trying to figure out where it is., but might use it with the sign for “where.”
“If I’m not back in 10 minutes call a plumber”
In Swahili you say “Wapi cho?” to inquire as to the whereabouts of the toilet. Which, I suppose would serve to announce your intention to relieve yourself.
Pakistan in English. Washroom or restroom.
Pakistan in Urdu. Ghusal Khana literally bathing/cleaning place. Often shortened to simply ghusal
And then there’s the elegant “I have to blow some snags”.