The only way to get images to stay put is to insert them In Line with Text. You can place images side by side if you use a borderless table, but if you want anything more complicated than that, you will have to follow the suggestions Stefan and John have offered.
Note that, depending on the version of Publisher you are using, you may be able to continue doing so. I'm using Publisher 2003 (and also have 2010 installed) and assume they will continue to function.