TeX/LaTeX display the real quotation marks by default: ` and `` are converted to opening quotation marks; ' and '' are closing quotation marks. You'll generally always see the curved quotes in the output, in the default font. You should always quote like
``this''
and not like ''this'' or "this", because that appears like ”this” (closing quotation marks on both sides), and is very annoying to readers. (If you type the double quote character in Emacs, it automatically guesses whether you meant to insert `` or ''; other editors probably do too.)
You can also directly enter the curved quote characters if you like, if you're using an environment that supports Unicode input: either \usepackage[utf8]{inputenc}, or XeTeX/LuaTeX. See the question on glyph insertion.