For information on how to edit your sidebar in general, see this article.
By default the sidebar is set to appear the same on all pages, however in some situations you may wish to have different sidebar contents on a particular page.
For example, lets say we wanted to change the sidebar on our About Us page without changing the sidebar on other pages. To do this log in to your dashboard and go to Appearence > Widget Areas.
Here you will see a screen that looks a lot like your Pages screen. This is where we can create custom Widget Areas to replace existing Widget Areas under certain conditions.
We begin by selecting Add New, at the top to the Widget Areas screen, right next to the Widget Areas title.
Selecting this will take us to the following screen:
This is the screen where we set up our new Widget Area. What we want to do is create a Widget Area to replace Sidebar 1 on the About Us page.
We'll start by giving the Widget Area a name. It's best to give it a name that best describes its purpose. In our example we're creating a sidebar for our About Us page, so About Us Sidebar is an ideal name. You can also give it a description. Generally this is not necessary, unless you are adding lots of Widget Areas and think you might forget what each one is for.
The most important sections are the Conditions and Sidebar To Replace sections. This is where we determine where and when this Widget Area will appear. As you'll recall, Sidebar 1 is currently the widget area whose content appears on our sidebar on the About Us page. What we want to do is replace Sidebar 1 with our new Widget Area, but only on the About Us page. Therefore we need to check the box next to About Us under Conditions > Pages, and choose Sidebar 1 under Sidebar To Replace.
Once these options have been set, click the blue Publish button on the right to create the Widget Area.
Now when we go to the Widgets screen we will see this:
We now have a new widget area called About Us Sidebar. We can now drop the widgets we want into this new widget area and they will appear on the About Us page's sidebar instead of Sidebar 1.
You can repeat this process as many times as you like to create unique sidebars for any of your pages, or you can be a little more advanced, and create a sidebar for a group of pages, by checking multiple pages in the Conditions section when creating your Widget Area.