One of Drupal's best features is taxonomy. This tutorial gives an introduction on how to use Drupal's taxonomy system.
New users to Drupal sometimes find taxonomy difficult to understand at first. I recommend reading all the way through this tutorial once. If the first part doesn't make sense, I hope that it will by the end.
Taxonomy can be thought of as categories or tags. Drupal taxonomy is made up of vocabularies and terms. A vocabulary is a set of terms and terms are just another word for categories.
The image below is from the taxonomy (categories) page located at http://example.com/admin/content/taxonomy:

Let's build the taxonomy for a news site as an example. First click on the Add vocabulary tab. You will then see a screen that looks something like the following image:

For Vocabulary name type in News. For Description enter Categories that fall in the news section of the site. For Help text, enter Please choose a section of the Web site for this news story.
Continuing down the page, you will see something like the following image. It will probably have fewer options than what you see below. The example below is from a site that has many different content types. If you are using a new Drupal installation, you might just see two content type options: Page and Story. For this tutorial, just check the box for Story and leave the rest unchecked. That means that only Story nodes can use categories from the News vocabulary (remember that a vocabulary is a collection of terms or categories).

The next part of the page has additional options:

Check the option Single hierarchy. That means that categories will be able to have a parent-child relationship, with only one parent for each child term. I'll explain that concept below.
Check the option Required. That means that every story node (news page) will have to be placed in one category of the site.
Leave the other options unchecked for now. Here is a quick explanation in case you would like to use them on your site:
After you have submitted the form as explained above, you will see something like the following screen:

The vocabulary has been created, but there are no terms categories in it yet. Click on the Add terms link.

For Term name enter Local. For Description enter Local News. Then click the submit button. You will be directed back to the same form where you can add another category. For Term name enter World. For Description enter World News.
After you have created the first two terms, create the third, but this time choose a parent category Local from the drop-down select box as shown below:

Name the term Sports. That will be the category for the local sports section.
Continue to add terms, in a hierarchical structure as shown in the outline below:
It will look something like the following image:

For optimal results, I recommend also setting up the Pathauto Module. Using the Pathauto Module with Taxonomy will allow you to automatically generate custom URLs that put each news item in a different section of the Web site.
After you have the Pathauto Module installed, enter the following setting for Story Paths:

The settings [vocab]/[catpath]/00[nid]-[title] will create news URLs that look like http://example.com/news/local/weather/0025-page-title and were chosen for the following reasons:
[vocab][catpath]local/weather.00[nid]-[title][nid] is the node ID which is unique for each node. Padding it with two leading zeros guarantees that the number will always be at least three digits. The [title] is the title of your post and it optional for people who want to include keywords in their URL.Now you have setup Drupal to have a news section that will automatically organize your content by category and generate nice URLs for you.
If you also want blogs on your site you could create a second vocabulary called Tags and choose the freetagging option. Also choose Disable Hierarchy. Make the vocabulary required by checking the relevant checkbox on the Add Vocabulary page. Associate the Tags vocabulary only with the blog post content type. Choose a URL structure in Pathauto—perhaps something like blogs/[user]/[cat]/[title] or blogs/[cat]/[title].
If you have questions, please leave a comment below. See also the Pathauto Tutorial for more information about how to make Taxonomy and Pathauto work together.
For more about Drupal Taxonomy, see the Drupal Taxonomy Handbook.
If you are interested in actually building a news site in Drupal, check out the writeup of the New York Observer project.