Supposing some strings (like 123 or abc or test123) would automatically appear on the screen after last command and I cannot know the exact value of the string in advance.
Next I want to make a new directory named after that string (like ./123/ or ./abc/ or ./test123/), which means the string should be given to a variable var so that the new directory could be created by mkdir $var.
You can use backticks to store the result of a command (in my example, it's uname) on a variable, then echo it onscreen, and eventually use it as argument to mkdir:
FOO=`uname -n`
echo "$FOO"
mkdir "$FOO"
The excellent Advanced Bash-Scripting Guide has a whole chapter about Command Substitution.
As @KalvinLee commented, the preferred format is now $(...):
FOO=$(uname -n)
$(...) syntax is worth considering. There's an explanation somewhere else on ULSE that I can't find now.
uname -n with the name of your random-string-generator command and you'll have what you want.