$field1=$yourArray['contacts'][0]['Id'] //Value 4229850
$field2=$yourArray['contacts'][0]['FieldValues'][4]['Value'] //Value 2011
Uso de métodos PDO
$sql = "INSERT INTO yourTable (field1,field2) VALUES (:field1,:field2)";
$q = $conn->prepare($sql);
$q->execute(array(':field1'=>$field1,
':field2'=>$field2));
Usando la función mysql_query
mysql_query("INSERT INTO yourTable (field1,field2) VALUES ('$field1','$field2')");