Pick a number between one and ten. Someone familiar with US practices would know that one and ten are included. A visitor to the US might think the range is two through nine, being between one and ten. What would be the best way to word the offer, so the visitor would not be at an unfair advantage in case the number to choose is one or ten?
You could say, "Pick a number from one to ten". This is usually understood to be inclusive - going from A to Z doesn't mean you start at B and end at Y, and working from Monday to Friday doesn't mean working only three days a week. Or, if you want to be extremely precise, say "Pick a number from one to ten, inclusive".
@Matt's answer is the way I've usually heard it, but one way to be even clearer that 10 is included is to use "through":
Pick a number from one through ten.
and you can emphasize that you're including the endpoints with "anywhere":
Pick a number anywhere from one through ten.
I'm not sure why Talmu deleted his answer, because I think it's correct and what I intended to say. If you want to be absolutely clear, you say "between one and ten inclusive" or "between one and ten exclusive".
The phrasing "between X and Y" is ambiguous on whether the end-points are included. If you said, "Al's scores were all between 8 and 10", I'd probably understand you to mean that he got some 8's, some 9's, and some 10's. But if you said, "Al's score was between Betty's and Carl's", I'd think you meant higher than Betty's and lower than Carl's, and not that it might have been the same as one or the other. It all depends on context, and is often not clear.
As others have noted, there are other phrasings that are not ambiguous. Like if you said "pick a number from 1 to 10", I think any English-speaker would assume that 1 and 10 are included in the range.