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matching {}

I have seen someone (Dan Brotsky) with his EMACS customized to
automatically insert a matching (, {, or [ after a ), }, or ]
(respectively).  The cursor is then left between the () to allow text
to be inserted.  Dan does this in his own macro file (which has other
features that I don't want and I can't figure it out anyway) and I
believe that other people have this in INIT files.

Can anyone help me get the appropriate code to generate the matching
delimiters?  I would like it for (), {}, and [].  I would also like it
for matching $$ if I can hook it to only happen in TEX mode.  If these
can not be hooked into TEX and LISP modes only, then I can live with
the keys always defined in this manner.

It seems to me that this feature would be handy to have in an EMACS
library--I would think that several people would use it if available.

Thanks for your help.