How to remove non-alphanumeric characters?

Sounds like you almost knew what you wanted to do already, you basically defined it as a regex.

preg_replace("/[^A-Za-z0-9 ]/", '', $string);

$str = preg_replace('/[^a-z\d ]/i', '', $str);
The i stands for case insensitive.
^ means, does not start with.
\d matches any digit.
a-z matches all characters between a and z. Because of the i parameter you don't have to specify a-z and A-Z.
After \d there is a space, so spaces are allowed in this regex.