It would depend on the situation, such as where I am and who I am with. If I am at home with a close friend or family member, I would just say, "I have to pee." (Or more accurately, "I gotta pee!" I don't always use correct grammar.)

These examples are all for simply stating that I need to use the bathroom, as a way to excuse myself for a moment. If I needed to ask to use the bathroom - such as if I am at the home of someone I don't know well - I would simply ask, "May I use your restroom?" (This feels more polite and formal than saying "bathroom".) It is sometimes phrased, "Do you have a restroom (or bathroom) I can use?"

Wow, I never realized how much context was needed to decide how to talk about going to the bathroom. Haha!

In American English, I believe it is considered rude (or too graphic) to use the word "toilet". I believe Americans use the following euphemisms instead:

"Excuse me, please, where is the restroom? / where are the restrooms?"

"I need to go to the restroom / to the ladies' room / to the little boys' room / to the bathroom."

In British English, we do use the word "toilet" and it is not considered rude to use it:

"Excuse me, please, where are the toilets? / where is the toilet?"

"I need to go the toilet"

"I need to go to the loo" (a British slang word for "toilet").

Important note about the word "bathroom" (as used in British English versus American English)

In British English, a bathroom is a room that contains a bath tub. It is a place where you go to wash. A bathroom may or may not have a toilet in it as well. If we want to use a toilet, we do not say "I need to go to the bathroom" in British English, because that would mean "I want to have a bath".

In American English, "bathroom" is used as a euphemism for "toilet". When Americans say that they want to go "to the bathroom" they do not actually mean a room used for bathing, that has a bath in it. Rather, they mean a room that has a toilet in it.

A side note about the term 'WC'.

Half the world seems to be under the impression that "WC or 'water closet' is how the British say 'toilet' ".  Just to set the record straight - this isn't true at all.

We don't use this term in the UK. A toilet is simply a toilet or more commonly, politely, informally, a 'loo'. You, may, very occasionally, see an old sign in a park or similar place with the letters 'WC' on it. But you will never hear anybody say 'WC'.

To Lily Earnes-Jevons:

"So you gotta watch your tongue in America, huh?"

"So you gotta watch your tongue in Canada, eh?"

We Canadians often use the term "washroom" as in "Where's the washroom please?"

But the term "eh" is a well known Canadian nuance.  In fact, it's even made it into the comedy stream on TV.  I'm from Canada, eh!  Our American "neighbours" (note Canadian spelling with a "u" which Americans omit") often use "huh."  I grew up along the Canadian, American border and teens from both countries would attend events together sometimes, many years ago of course.  I had close American friends and, on occasion, we would banter and joke about "eh" and "huh."  "How's Canada, eh?'  "It's the best... how the United States, huh?"  All in fun, of course.

It's off topic a bit, but I wanted to touch on a small cultural nuance among "neighbors" (note American spelling). 

Good luck to all with your learning goals.