I don’t think you know what ASCII characters are.
The ASCII character set was invented in the USA. The printable ASCII characters correspond exactly to the characters on the keyboard on normal North American English keyboards.
See http://en.wikipedia.org/wiki/ASCII .
The ASCII character set was used on every micro-computer often with extra characters that differed from machine to machine. “ASCII art” was originally so named because when making it one limited oneself to the ASCII (keyboard) characters so that the result could be displayed on any micro-computer.
I think you may mean “non-ASCII characters”. For the characters, see the official Unicode charts at http://www.unicode.org/charts/ and the character charts at http://www.alanwood.net/unicode/#links . There are too many characters in Unicode for any one font to contain them all. You must have a character in at least one font on your system in order to see it and often must set your current font to that font in order to see it.
Browsers usually have some degree of automatic font substitution where if the character is not found in the font that the browser is currently using, the browser will search through every Unicode font on the system, and if it finds the character will display it in one of those fonts. Firefox appears to do this best.
For entering non-ASCII characters, see http://en.wikipedia.org/wiki/Unicode_input , and http://scripts.sil.org/cms/scripts/page.php?&cat_id=InputResources , and http://ipa4linguists.pbworks.com/w/page/4325768/FrontPage .
The standard Alt key method only gives you a very small number out of all the characters available. It was originally intended to allow you to get every character in the set, in the day when character sets were limited to 256 characters.