Along with what @Chris_O said, when you are in the editor for the pictures select Left on one and Right on the other. This applies the alignleft and alignright classes, respectively.
Your theme has to have the CSS classes defined, if you have one from vendor, they are more then likely there, but in case they aren't, just go into the theme editor and add them to the CSS:
.alignleft {float:left;}
.alignright {float:right;}
I also like to add something like this for the images I float, since the test might wrap around them;
img.alignleft, img.alignright {
padding: 5px;
display: inline;
}
Obviously you can add margin or changing the padding to suite your taste.
<br />tag or just unwanted whitespace? It could actually be a theme CSS issue, and not a WordPress editor issue ... – EAMann♦ Aug 22 '10 at 14:34