Upgrading Drupal from one minor version to the next can be time-consuming and error prone. A lot of folks use Drush for this, but a good second choice for the commandlinophobic is to use a patch file.
First, go to your sites /admin/reports/updates page and see what version of Drupal you're running. Here's what mine looks like:
So, I'm on 6.16 and need to upgrade to 6.17.
Next, go to the list of patch files and find the one that matches up with your version. Click on it to download:
Move the downloaded patch to your Drupal site's base directory.
Now, we need to move to the command line. Sorry, commandlinophobes.
First, cd to the directory where you just put the patch file.
Before we run the patch for real, we're going to do a quick dry run to make sure that we don't get any errors. You'll need to use the actual patch file name you downloaded:
patch -p1 --dry-run < drupal-6.16-to-6.17.patch
You'll see a list of everything that gets patched. If you see any errors having to do with HUNKs, then you should probably use another method to upgrade.
If everything looks good, then run the patch for reals:
patch -p1 < drupal-6.16-to-6.17.patch
Now, run /update.php.
Update: Check out an article Kalid posted in the comments that shows how to automate this process via the command line. It's more command line-heavy, and if you're going to get that heavy it's just a tiny step over to using Drush, but is still pretty cool.
Here's some additional information about upgrading if you run into issues:
* The drupal.org handbook page on upgrading with patches
* The drupal.org handbook page on upgrading in general
* The list of patch files
* Also reference the UPDATE.txt file in your Drupal site's main directory for more information