First make a string with all your possible characters:
$characters="abcdefghijklmnopqrstuvwxyz0123456789";
You could also use range() to do this more quickly.
Then, in a loop, choose a random number and use it as the index to the $characters
string to get a random character, and append it to your string:
$string = '';
$max = strlen($characters) - 1;
for ($i = 0; $i < $random_string_length; $i++) {
$string .= $characters[mt_rand(0, $max)];
}
$random_string_length
is the length of the random string.