How can I use parameter expansion? How can I get substrings? How can I get a file without its extension, or get just a file's extension?

Parameter expansion is a separate section of the bash manpage (man bash -P 'less -p "^   Parameter Expansion"' or [ see the reference]). It can be hard to understand parameter expansion without actually using it. (DO NOT think about parameter expansion like a regex. It is different and distinct.)

Here's an example of how to use parameter expansion with something akin to a hostname (dot-separated components):

parameter     result
-----------   ------------------------------
${NAME##*.}                         champion
${NAME%%.*}   polish                        

And, here's an example of the parameter expansions for a typical filename.

parameter     result
-----------   --------------------------------------------------------
${FILE}       /usr/share/java-1.4.2-sun/demo/applets/Clock/Clock.class
${FILE#*/}     usr/share/java-1.4.2-sun/demo/applets/Clock/Clock.class
${FILE##*/}                                                Clock.class
${FILE%/*}    /usr/share/java-1.4.2-sun/demo/applets/Clock            

You cannot nest parameter expansions. If you need to perform two separate expansions, use a temporary variable to hold the result of the first expansion.

You may find it helpful to associate that, on your keyboard, the "#" is to the left of the "$" symbol and the "%" symbol is to its right; this corresponds with their acting upon the left (beginning) and right (end) parts of the parameter.

Here are a few more examples (but please see the real documentation for a list of all the features!). I include these mostly so people won't break the wiki again, trying to add new questions that answer this stuff.

${string:2:1}   # The third character of string (0, 1, 2 = third)
${string:1}     # The string starting from the second character
                # Note: this is equivalent to ${string#?}
${string%?}     # The string with its last character removed.
${string: -1}   # The last character of string
${string:(-1)}  # The last character of string, alternate syntax
                # Note: string:-1 means something entirely different.

${file%.mp3}    # The filename without the .mp3 extension
                # Very useful in loops of the form: for file in *.mp3; do ...
${file%.*}      # The filename without its extension (assuming there was
                # only one extension in the first place...).
${file%%.*}     # The filename without all of its extensions
${file##*.}     # The extension only.