You really should only sendmail through some kind of server-side program (php/asp/cgi). As stated before, javascript can't do it. Fsze88 said you can use a mailto: target which is true, but that puts the burden of send the mail on the client, and client machines aren't reliable enough for that. If they don't have Outlook or Outlook express or Thunderbird setup properly, it won't work.
CGI is the predecessor to modern web programming (php/asp/jsp). A cgi-bin folder is simply the place you would put your programs that get run by the server. I would think almost all webhosting plans provide cgi-bin access, even though it isn't very popular anymore. Cgi-bin is just a folder, you don't really "assign an action" to cgi address, you put your cgi programs in that folder and call them like any other webpage:
http://yourdomain.com/cgi-bin/yourprogram?arg1=value1&arg2=value2There are thousands of free scripts out there (cgi and other languages) that can do the emailing for you. Look around for some.
http://hotscripts.com