You just do an include like you normally would. For example, a "normal" include would look like this:
include("file.php");
Or if you want to do a variable, like you suggest, then it's the same idea:
$file = "file.php";
include($file);
You won't want to use single quotes around the variable name because that will cause php to treat the variable as just the literal name (use double quotes only to have the variable interpreted). Of course, like in my example, you don't need to use quotes at all for the variable.