From the MathCentre this very clear nine page leaflet describes symbols and notation in common use in Mathematics, for each symbol we learn what to say, what the symbol means and where appropriate an example is given; it is also possible to search the Math Centre site for further details.
If you are wondering how to pronounce any symbols, this chart of common pronunciations should help. I am pleased to see that the pronunciation of sinh x is given as shine x as there have been a few arguments over this one!
If you are looking for a particular character you could use a WolframAlpha query, or check this comprehensive Wikipedia entry on Mathematical Symbols. There are some very useful documents here and also links to external sites.
From the University of Nottingham Sixty Symbols (there’s actually more than 60!) has a collection of videos about the symbols of Physics and Astronomy.
From Penn State you can find many symbols here, I found that I can just copy and paste the symbols, for example:
ℝ ℂ ℕ ℙ ℚ ℤ
∀ ∃ ∧ ∨ ∩ ∪ ∊
One can of course also insert a symbol in a program like Word: ≅ ∴ ∮ R
A very easy to use site is copypastecharacter.com, just click to copy a character. Several sets are available, note the drop down menu. It is possible to save your favourites from the sets here by creating an account; I created a set which you can see here.
If you want some calculator buttons in your documents, from Casio a variety of Fonts to download for teachers:
In response to a query I have created an Excel spreadsheet which lists ascii characters.
You can then copy the first column as many times as you wish and then simply change the column to your desired symbol font.
The spreadsheet has EOS3, EOS4 and the Wingdings fonts.
See this Excel Zoom post for a simple way to see all the characters in a font – one simple command can generate all 255 symbols!