This series could be titled A Regular TypePad User Dabbles In WordPress. As you read, please keep in mind that there are many, many people here who know much, much more about WordPress than I do.
However, curious about all the recent commotion over problems with inserting images in a WordPress post, I set up a test WordPress.com blog http://cheryljns.wordpress.com/ and started playing around.
First off, I found that simply using the Firefox browser instead of Internet Explorer resolved many of the image positioning issues.
But for those who, in Tina Turner's immortal words, "never, ever seem to do anything completely nice and easy", here is my "nice and rough" beginner's version of positioning images with the WordPress code view.
1. Write something.
2. Upload first image. Show: Full size Link to: None Click: Send to editor

3. Don't touch the image icon. Click on the Code tab.

4. In the HTML code, note the tag that starts with <img src ... that is the HTML code for inserting an image.

5. Edit just this one tag, by adding align="left" between the <img and the src. Hit Save and continue. After saving, WordPress will return to the Visual view. Click on the Code tab to return to the HTML code.

6. It looks to me that when using Internet Explorer as your browser, regardless of when your cursor is positioned, WordPress will add the image code at the top of the Code view window. But, go ahead and place the cursor at the very beginning of the top line of code.
7. While still in Code view, upload the next image. See how the code for that image is now the first thing at the top in the Code view window? It's easy to recognize anyway, it's the one without the align="left" that we just added between <img and src.

8. Drag the mouse over the code for that new, second image. Start at the first < and end at the >. Images won't work without their angle brackets. (But if you accidentally miss or delete an angle bracket, you can always type it back in.) Hit Edit -> Cut

9. Find the paragraph where you want to include the second image. Position your cursor at the left side of one of the lines of text in the paragraph. Hit Edit -> Paste. For this image, try adding align="right" between <img and src. Hit Save and continue.

(Analytical people will notice the screen shots were taken at different times with slightly different text, You're right, they were. <s>)
Question for WordPress people: Did the WordPress - Internet Explorer image positioning issues just start with the latest version of WordPress?
P S -- For anyone who does not know me. I'm actually not a rank beginner. I am a long time TypePad user. See: http://www.nelalive.net/ || http://www.taylorhotsheet.com/ || http://www.dablogmother.com/
I really don't have any business writing about WordPress. But after reading Mike Jones comments about WordPress multiple photo issues, I thought I'd experiment with Wordpress (just for the h#ll of it).
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Cheryl - post like yours is what I found to be priceless about AR- where else people would take the time to provide this great information. Now, I was considering starting a second blog using Wordpress.org and suspected that it will be more then I want to deal with for the set up. I thought that posting would be as easy as on AR. From your post I am not sure any more. If to load a picture, I would have to change HTML code, that I don't know to begin with, should I not even think about using Wordpress.org? Thanks.