How to see which fonts a PDF uses
List a PDF's fonts in PDF by Zaweba from Document properties: each font's kind, whether it is embedded or a subset, and where in the file it is used.

Open Document properties with Ctrl+D and choose List the fonts. PDF by Zaweba then shows every font in the file with its kind, whether it is embedded or only a subset, and where in the document it is used. It takes a few seconds and answers most font questions before they become problems.
Fonts are behind more PDF trouble than people realise. A print shop rejects a file because a font isn't embedded. Text looks different on someone else's PC. An edit to a word comes out in the wrong typeface. Knowing exactly which fonts are in the file is the first step to sorting any of these out.
What the list tells you
The name of each font is the obvious part, and often all you wanted: you liked the look of a brochure and want to know what it was set in.
The kind of font says what sort of font file it is. That matters mostly to printers and designers, but it can explain why a font behaves differently from the others.
Embedded or subset is the key detail. An embedded font travels inside the PDF, so the page looks the same everywhere. A subset is embedded too, but only with the characters the document actually uses. That keeps files small, and it's normal, but it has a consequence when you edit: if you type a letter that wasn't in the subset, there's no shape for it in the file. A font that isn't embedded at all relies on the reader's PC having it, and if it doesn't, something else is substituted.
Where it's used tells you which parts of the document each font appears in, which is handy when one odd font has crept into a single heading.
Opening the font list
Open the PDF. Press Ctrl+D to open Document properties. Choose List the fonts. Read down the list, paying attention to any font that isn't embedded.
Fonts before print and editing
Before sending a file to print, check that every font is embedded or subset. A font that isn't embedded is the thing print shops most often flag.
Before editing text, check whether the font is a subset. If it is, small changes using letters already in the document work fine, but new letters may not be in the file. PDF by Zaweba edits the text of real-text PDFs, and knowing the subset situation helps you predict when an edit will match the surrounding text.
If text looks wrong on screen, a missing font is the usual cause. The list will show the font isn't embedded, and the fix is to ask the sender for a version with fonts embedded, or to install the font on your PC if you have the right to use it.
Other things in Document properties
The same window holds the document's title, author, subject and keywords, which you can edit. Those are what appear in search results, file browsers and the window title of many PDF readers, so they're worth setting on anything you publish.
File > Additional metadata (XMP) goes further, editing common fields and listing every property, with import and export of .xmp files. File > Custom properties lets you add your own fields, such as a project number.
Checking fonts is a quick habit worth forming, and in PDF by Zaweba it's one shortcut and one click. The app works offline, so you can inspect a client's file without it leaving your PC.