Display posts that are related by category in sidebar

I am a new WordPress user using the Verticle theme by dessign.net.
When a visitor opens a post, a group of posts are displayed in a sidebar to the right. Currently, these posts are chosen at random. I would prefer that the posts shown in the sidebar share at least one category with the post being viewed so that the content is related. Others have posed similar questions but I have not found a clear answer to mine. I believe I must alter the sidebar.php file and I think specifically the line that reads: ‘orderby’ => ‘rand’ however I doubt it is as easy as changing ‘rand’ to something like ‘category’. Please advise.