To add images, audio, or other files from your computer (as opposed to things you find on the web), use the Add Media buttons at the top of the post editor.
When you get to a point in your post where I want to add audio, video, or an image to my post, place the cursor where you want the media to be, and click one of the gray media buttons at the top of the editor. There are buttons for images, video, audio, and other files, and they all work the same way; this post uses an audio file to demonstrate.
The Add Audio window comes up, and there are several choices: you can add files from your computer, from a URL on the web, or you can use a file that’s already in the media library for the blog.
To add a file from your computer, choose “Select File” and browse to find your file.
Once the file is uploaded, check that the information looks correct, edit if needed, and then click “Insert into Post” at the bottom of the window.
One note: this process is only for files that are small enough to upload to your blog. Most audio files, images, and documents will work, but videos more than a few seconds long should be hosted on a video site like YouTube or Vimeo.