I recently purchased Site Designer as my current software is no longer supported.

I have been using it for many tears and it is very easy.

Text boxes, images etc can be placed on the canvas and resized by moving the edges or corners. They can also be dragged into the desired position. It's so easy.

I don't seem to be able to do this on site designer.

Am I missing something?

Seems to mee you are missing your old software

It's a different way to do that in Site Designer
Dragging elements onto the canvas is easy enough simply drag & drop,, getting more elements into a parent element (nested container, text, images etc can be done by dragging & dropping or use the "inspector: tab to place them wherever you want them to go

If you use the "inspector" tab then on the top bar of sight designer is the "HELP" tag open that and there is a tag for KEYBOARD SHORTCUTS

they can help you move any element up or down

I am doing a demo for another user at the moment (not exactly your problem,, but I can include what you are wanting to do,,it will be a little while yet,, in the meantime there is also in that "HELP" tag a section for GUIDES VIDEOS etc,, if you open that (videos)there are a number of nice videos there explaining plenty of stuff including what you maybe looking for,,