Just in case, though, here's a quick run down of the basics:
US pants = UK trousers
US vest = UK waistcoat
US suspenders = UK braces
If you want to talk about your underpinnings in the US, you can say underpants, underwear, or possibly "skivvies" for slang. Knickers, confusingly, are a knee-length trouser-type item more like knickerbockers. Panties are panties, but nobody wants to have to say that.
A (UK) vest in the US is an undershirt, and suspenders are a suspender belt.
In the UK/Ireland, a shirt is only a long- or short-sleeved article of clothing that has buttons all the way down the front - made of material which generally calls for you to bust out the iron. A t-shirt is a short-sleeved, collarless top of softer jersey material. Anything else (in womenswear, at least) that is a first-layer item (not counting a camisole, or a thermal vest, depending on the season) falls under the general heading of "top", with qualifiers like "long-sleeved top" or "going-out top" or "sleeveless top".
In the US, the word "shirt" can be applied to almost anything you wear on your top half, short of a sweater. And sweater covers everything else, whether it's a giant, slouchy thing with a sporting logo on it or a cosy cashmere turtleneck, or even a cardigan. (Though those other words are applicable too.)
Which brings us to jumper.
I was bemused, one day in Ireland while watching The Simpsons, to hear Bart being teased by his sister, who said something about his needing to wear a jumper. This didn't sound like such an awful fate, because as far as I was concerned, a jumper is a knitted sweater - but with a leap of great mental acuity, I surmised that there was more to it in the USA. Many moons later (this was before the advent of the Internet to my house, or anywhere handy, I suppose) I figured it out: a jumper in the US is what I would call a pinafore - a dress that goes over a shirt (or top), the sort of thing that's often part of a girl's school uniform.
Have I forgotten anything?
I leave you with this gem of Irish pop. If you don't know a boy who left his jumper in some dark corner of the disco and now can't find it, well, you probably haven't been to an Irish disco yet.