There are several ways to add PHP snippets.

Adding a PHP snippet by editing a PHP file

Many PHP snippets are added by directly editing a PHP file in your Drupal directory. To do this, you need access to the files (for example, using Telnet/SSH, FTP, or Cpanel's File Manager).

After you add a snippet for the first time, you may see this error:
Parse error: syntax error, unexpected '<'

This error usually occurs because unwanted php tags were not removed from the new snippet. On Drupal.org PHP snippets are usually presented with '<?php' at the beginning, and '?>' at the end. They look like this:

/** The actual snippet starts on this line. But this line is just a comment, it doesn't do anything */
function do_very_complicated_stuff ($drupal) {
  $inexplicable = confusing(
etc...

/** The snippet ends here. This line is just a comment */

PHP snippet authors put these tags in because it makes Drupal.org display PHP with helpful colored syntax highlighting. To prevent PHP syntax errors, when you add the snippet, delete these two PHP tags from the beginning and the end of the snippet (don't delete any other <?php or ?> tags in the snippet or in the file you are editing).

Adding PHP snippets through the Drupal user interface

Sometimes you don't need to directly edit files to add a PHP snippet. You can use the administration interface to insert PHP snippets into certain sections of the page. For example, PHP snippets can be included in specific blocks, nodes or views in this way. Some PHP snippets are designed to be used in this way and may not produce the expected results otherwise.

To insert PHP snippets this way, you need to make sure the PHP input filter is enabled. Go to Administer › Site building › Modules, or via the http://yoursite/?q=admin/modules and check PHP Filter under core - optional.

Now when you create new content, a PHP option should be available under input formats - you must select this when you paste in a PHP code snippet. If this option does not appear, the account you are using may not have permission to use this format, go to Administer › Site configuration › Input formats and select configure next to the PHP code option. You might also need to visit Administer › User management › Permissions. Only allow trusted administrators to use the PHP input format.

If you've replaced the standard Drupal text area boxes with a rich text editor such as FCKedit or TinyMCE, click the Source (FCKedit) or HTML (TinyMCE) option on the editor's toolbar before you paste in PHP code. If you don't do this, you'll just see the PHP code itself appear on the page.

You probably do not need to remove the initial and closing PHP tags when you add a PHP snippet to your site this way. For example, PHP snippets used in 'Page specific visibility settings' for blocks do require the tags.

See also: How to insert and use the PHP Snippets in your pages. (from 2005 - may be out of date) http://drupal.org/node/23223
How to use views snippets http://drupal.org/node/75959
How to use PHP Snippets with the front_page.module http://drupal.org/node/23224

Adding more than one PHP snippet

Using multiple PHP snippets. (This is from 2005, so it may be out of date. The comments provide more up-to-date information): http://drupal.org/node/24258