There are 2 different ways to preview your Markdown files in Apostrophe and quickly check, what you have written.
If you have e.g. math, you can open the context menu with a right click on your formula and will get a quick preview of your equation inside the context menu. This will work not only for math, but also for links, footnotes and images.
If you want a complete Preview of your document, you just need to hit the preview Button on the statusbar at the bottom of the Apostrophe window. It will render the complete HTML Output of your Markdown file.