// always initialize a variable before use!
$conditions = array();
$parameters = array();

if (!empty($_POST['myparam'])) {
    $q1 = trim($_POST['myparam']);
    $q_myvar = $q1;
    $conditions[] = 'mycol = ?';
    $parameters[] = $q_myvar;
}

$q = "SELECT * FROM mytable";

if ($conditions)
{
    $q .= " WHERE ".implode(" AND ", $conditions);
}

$stmt = $conn->prepare($q);
$stmt->execute($parameters);
$data = $stmt->fetchAll();