Can you supply a screenshot of what you're trying to do?
Possibly you must set the Runaround properties to Don't Run Around. Then the text will stick where it is.
I suggest you use the text frame tool (to the left of Arnis' supplied screenshot) and set the background of the text frame (the diagonal b/w lines below the text frame tool) to None.
When all else fails, add the text to the graphic, save as PDF or other appropriate format, and place as needed.
Matt R. Sullivan
co-author Publishing Fundamentals: Unstructured FrameMaker 11
It's not clear what the page looks like when it's jumbled.
Also, in your next screen shot, please turn on View > Text Symbols, and View > Borders, to make troubleshooting a bit less speculative.
It's possible that there are other currently-invisible items on the page with runaround properties that are affecting the text.
I figured it out! Thanks to everyone for all the helpful suggestions.
The issue was that the image itself had runaround properties. I had been resetting the runaround properties of the text only, and not the image. I didn't realize you had to do both.