Have a look at your theme files - inside your current theme folder you will probably find a document called 'page.php' - this is the file used to display 'Pages' (NOT POSTS!) - if you don't have one you can usually just duplicate 'index'php' (depending on your theme), rename it 'page.php' and save and upload it to your server.
Then just delve into the code and if you don't want the date (and it shouldn't show category if it is a page anyway) just look for something that looks like this:
<?php the_time('l, F jS, Y') ?>
Posted in <?php the_category(', ') ?>
... then just delete these out of your new 'page.php' file and you should be sorted!
JUST REMEMBER TO BACKUP YOUR THEME FIRST!! Have a go, you are going to find it very hard to break anything if you just stick to modifying theme files!
Oh, you may also find this link helpful as it outlines what files get used where: