How do I place the field in a particular section and have it stay there?

When I click on the field and move it, it pops into a space that I don't actually need it to or it returns to the previous place. 

You can just drag and drop the fields to the location where you want it to be. I would suggest you to select the field first and then hover your mouse to field until the "Move" cursor appears. After that, you can just drag it where you want it to be. Here's a screen capture:

Related guide: https://www.jotform.com/help/328-How-to-position-fields-in-JotForm

If you have any questions, let us know. Thank you.

We are dragging and doping BUT it bounces to where ever it wants to go. It does not remain in the place we want it to. We have been trying for a few days now.

I also could not reproduce the problem you were having on the Form Builder. Drag & Drop method in positioning the field is working well for me.

It could probably a browser related issue on your case. Please try also refreshing or restarting your browser. Or if you have other browser you can use to test, please try also. See if these process makes any difference.

Alternatively, you can position the fields without using the drag & drop method. You can select a field and then click another field in the list. The new added field will always be positioned after the selected field.

Hope this help. Please let us know if issue persist for you.

Thanks.