Rewrite URL in .htaccess just cause 404 error - php

Question

I'm trying to learn how to rewrite URL in the .htaccess file. I have read some tutorials, but despite that I write as in the example code, nothing happens for me! I'm wondering what I'm doing wrong here? I get a 404-code when I'm trying the code below.
RewriteEngine On
RewriteRule /byggnader/1/ /?p=byggnad&id=1
This is just a test and I wonder if /byggnader/ must be an existing file or just a name in the URL. I'm using a page controler design. So URL /?p=byggnad&id=1 will open the PSelectedBuilding.php file inside the index.php file.
I preciate some feedback to be able to continue.
EDIT: Since it's not working despite the help below, I also add the code from the index.php file that handle the requests. Perhaps that could give a clue why!?
<?php
session_start();
// Allow only access to pagecontrollers through frontcontroller
$indexIsVisited = TRUE;
require_once('config.php');
// pagecontrol
$page = isset($_GET['p']) ? $_GET['p'] : 'start';
switch($page) {
case 'start': require_once('PIndex.php'); break;
case 'karta': require_once('PMap.php'); break;
case 'byggnader': require_once('PBuildings.php'); break;
case 'tips': require_once('PTips.php'); break;
case 'visa-byggnad': require_once('PHandleSessions.php'); break;
case 'byggnad': require_once('PSelectedBuilding.php'); break;
case 'visa': require_once('PSelectedBuilding.php'); break;
case 'visa2': require_once('PHandleSessions.php'); break;
default: require_once('PIndex.php'); break;
}
require_once("CreatePage.php"); // Call file that creates the page
?>
EDIT 2:
This works fine, but not when I'm using requests for some of the pages:
RewriteEngine On
RewriteRule bilder-byggnader-kopenhamn /?p=byggnader
RewriteRule karta-byggnader-kopenhamn /?p=karta
RewriteRule start /?p=start
RewriteRule tips /?p=tips

Answer 1

Remove leading slash from your rule. .htaccess is per directory directive and Apache strips the current directory path (thus leading slash) from RewriteRule URI pattern.
RewriteEngine On
RewriteRule ^byggnader/1/?$ /?p=byggnad&id=1 [L]

Answer 2

Try this one:
RewriteEngine On
RewriteCond %{QUERY_STRING} p=(\w+)&id=(\d+)
RewriteRule ^index.php /%1/%2? [R=301, L]
The RewriteCond mathches the Query String (as per your wish) extracting two variables which you can reuse to build your redirection target in the rewrite rule directive. The final question mark tells Apache not to reappend existing QS. R=301 says that the redirection is permanent, L that this is the last rule to be processed.
You may have to play with the index.php part since you never put the REQUEST_URI part in your question.