How do I change the layout of my shop and category pages?

Use Settings → Appearance → Shop Templates (the all-products page) and Category Templates (every category page). Both work the same way:

1. System templates are ready-made and read-only. Click Activate on one to use it straight away.
2. To customise, click Clone on a system template (or Add Templates, give it a title and pick one to start from). Your copy appears under My templates.
3. Click Edit to open the builder, rearrange the blocks, check the live preview, then click Save Layout.
4. Click Activate on your template to make it the store default.

A template controls the order of blocks. The sidebar position, products per row and title style still come from Catalog Settings. Category templates preview a real category, so you need at least one published category.