As of 2017, the Insert Image feature has been updated dramatically to include a thumbnail gallery and other features. Please see the Image Gallery article for more details.
Including images with your posts is a fun and easy way to add extra personality to your blog. First, you will need to save the image to your computer. Then you can upload the image to your Typepad account for display online. Images should be in GIF, JPEG, JPG, or PNG format.
Directly above the content area on the Compose page, you will see the Insert Image icon in the Rich Text toolbar: 
Uploading an Image
Use the Insert Image tool to upload an image to your post. You can use the default settings or click on Custom to set your own preferences.
When the Insert Image window opens, use the Browse button to locate the image on your computer. The Image Size option will allow you to choose a standard size or enter in your own custom size, in a pixel width. The Full size image option will scale the image to fit the width of the main, post column on your blog. The Text Link option will create a textual link to the full size image, without a thumbnail.
You can float the image to either the right or left of your text, so that the text will wrap around it. Or you can choose No Wrap so that the image is on its own line.
The Pop-up Window option will link the image in your post to the full size version of the image in a pop-up widow when it is clicked.
If you would like for the settings you've configured to be the default, choose the "Save settings as this blog's defaults" option. You can always use the Custom option again later to change these settings.
Finally, click the Insert Image button and the image will be uploaded to your account and displayed in your post.
After an image has been inserted into the post, you can add a caption, resize the image, change the alignment, or add special effects by double-clicking on the image in the Rich Text editor.
See the article on editing images in posts for more information.