Anglophone Nations
United Kingdom
On your first visit to the USA from the UK, you will probably think there will not be a language barrier and largely you shall be correct: an American can certainly read 98% of what you write down. With speech, it can be harder: the standard accents for America and Great Britain diverged sometime in the late 17th century and have remained on different courses ever since, plus the U.S. has been more consistently bombarded with influences from other tongues brought by immigrants since birth and continuing to the present: there will be idioms and ways of speech that will baffle and amaze both sides in any conversation.
If you travel to some of the tourist hot spots - like Florida or New York City - you will be one of a million tourists and should have no problem. Other places, like the Midwest, Rockies, and portions of the South, and you may need to speak slower than at home, especially if you make your home outside Southern England. The reason is that the accents found in these areas of England are what Americans associate most with the UK owing to the fact that these are the ones that have been featured in film, television, newscasts, and theatre for over a hundred years on both sides of the Atlantic; both the BBC and American media market have featured these accents for far longer than the others (Brideshead Revisted and Simon Cowell have not helped.) Whereas this has been changing in America for the last fifteen years, bear in mind it is still quite new and it is just as frustrating for them to understand as it is for you to be understood.
What you sound like
To American ears there are accents that will absolutely place a person as from the UK. Most notably included and better known of these are RP, Brummie, Leeds, Cockney, Scouse (Liverpool), and West Midlands when discussing England. Northern Ireland has a distinctive sound that has a slight lilt reminiscent of its southern brothers in the Republic but with a few traits and idioms closer to Her Majesty's English, and Scottish is most recognizable of all, very distinct indeed: to the American ear, there is a definite rolled "r" that evokes memories of "Bond, James Bond." (If a lady asks you to say this in a pub take it as a compliment and order a martini immediately-she fancies you.) Other accents are much harder to place as they may resemble some of the ones above: Welsh, for example, is hardest because it is one of the least heard and also has the rolled "r" and similar vowel pronunciation to American ears as Scottish!
Some accents from rural England will place you there but not always the right part: American ears will pick up on non-rhotic "r" (dropping the letter r when it doesn't begin a word, "Harvard" will sound closer to RP's HAH-Vudd rather than American English's HARR-verrd) but might have trouble hearing the difference between a Canterbury suburb and somebody living near Nottingham.
What to do
If you are having a difficult time being understood, try remembering what Tobey Maguire sounds like and imitiate him, and pay attention to where he puts his r's : Maguire was born and raised in California and this is an accent often heard on American TV and especially in movies. He is the best match as it is easiest for everyone to understand. Whatever you do, never try to imitate a New York accent (Robert DeNiro.) It may be tempting, but this is a no-no. (Many have tried, but alas it usually comes out as an odd hybrid.) Be patient-most Americans are friendly and happy to lend a hand.
Republic of Ireland
Congratulations! You are from a country that has exerted enormous influence on American politics, literature, and people: one U.S. citizen in five can trace his or her roots back to Ireland, some (particularly in New York and Massachusetts) with parents, grandparents, and great-grandparents either living within Ireland still or having emigrated as recently as the 1980's. You also thus have a brogue that will make American ears prick up and think "Irish! Definitely Irish!" like a dog hearing the dinner bell. You will, however, encounter some barriers similar to your UK counterpart above, mainly with idioms.
What you sound like
Your accent sounds unique to any of your immediate geographical neighbours, and to some Americans you sound "just like great-aunt Moira." You prononce the letter "r" much like most Americans do: "Parking garage?" will be easily heard and answered with "Five blocks down, Ma'am." However, by their reckoning, you tend to speak faster than most Americans can understand what you are saying-SLOW DOWN! The goal is to be understood, not to hop up and down in frustration and shout when you aren't and consequently possibly speaking even faster.
Furthermore, most Americans can easily pick out an Irish brogue but not necessarily which part of Ireland it is from, similar to how a Connecticut man will sound almost identical to a man from upstate New York to a visitor. Be patient, gently correct them, and if they are interested show them a photo of home-it can be a talking point later.
What to do
Idiomatic speech is clearly different in America, and although you get a steady diet of theirs they may not know all of yours yet: if you tell a shopgirl the dress is to "tarty" she will think something along the lines of it somehow making you hungry, not that it is too revealing! (Tarts are exclusively food, not people.) Similarly, a sign in Disney World will say "fanny packs: $25 each." It means they are selling a pouch like contraption that fits below the navel and fastens around the back with two nylon straps (eg, similar to a moneybelt.) It has nothing at all to do with Mum's privates and would be rather odd if it did as plenty of Dads are wearing them on the way to Pirates of the Caribbean with the camera inside.
Australia and New Zealand
You have survived the incredibly long flight to Los Angeles or the even longer flights to points elsewhere in America: for this, you deserve a medal let alone a good place to lie down and adjust to crossing multiple time zones. Most of the time you will be teased for sounding like Steve Irwin or Paul Hogan, unfortunately, but the majority of it is a gentle ribbing: so long as you do notwear zookeeper khakis and do not say the words shrimp or barbie in the same phrase, all shall be well.
What you sound like
Australia and New Zealand sound extremely, uncannily, and maddeningly similar to American ears-it is similar to how some have trouble telling the difference between a Canadian and American accent. Many a Yank has accidentally provoked a fight for mistaking a Kiwi for an Aussie: it is totally unintentional and rarely meant to cause offense (it may preclude you from hearing a heartfelt apology, see picture below.)
An American will, however, be eventually be able to pick an Australian out because Australian slang uses more diminutives, especially ending in -ie.
What to do
New Zealanders, do not get too angry if you are mistaken for your neighbours: it is NEVER meant to hurt your feelings and more likely mentioning Whale Rider or Lord of the Rings will help you point out you are definitely NOT from Australia and actually might give some Americans a frame of reference as to what home looks like vs what Australia looks like, especially if they come from a more rural area of the country.
Australians, try to curb using diminutives too often as it may confuse some Americans: some may think you are looking for an incredibly tiny or very young version of whatever something is! (For example, if you are visiting California and casually mention your friend is a "surfie" they will start looking towards your feet: they will anticipate something about the size of an Oompa Loompa walking up with his tiny, tiny surfboard to catch some waves.)
