Simple: you have to escape (take away special meaning) the quotes.
XXX=\"xxx\" echo $XXX
You may also use single quotes. Everything inside is taken literally, without any special meaning, ie XXX=' "xxx" '
If you want to surround text with single quotes, you have to use the backslash escape method.
bash(1) # that is the man page in section 1. Try man bash
bash info documentation
Advanced Bash Scripting HOWTO (start out simple. See www.tldp.org