How to add a note to a PDF
Put a sticky note on a PDF, or type straight onto the page, with PDF by Zaweba. Both are in the Comment menu and stay editable until you flatten them.

Use the Comment menu in PDF by Zaweba to add a note to a PDF. Sticky note puts a small note icon on the page with your text inside it, and Type on the page lets you click anywhere and type words that show directly on the page. The app is free, works offline on Windows and needs no account.
Which one to use depends on whether you want the note out of the way or in plain sight.
Sticky note or type on the page
A sticky note is discreet. The page shows only a small icon, and the reader opens it to see what you wrote. It's the right choice for review remarks, questions to the author and reminders to yourself, because it doesn't cover the text underneath.
Type on the page is direct. Click where you want the words and type; they appear on the page itself as a comment. It suits adding a missing detail, labelling a diagram, or filling in a gap on a form that has no fields.
There are two close relations in the same menu. Text box places a box of text on the page, and Callout adds a text box with a leader line and arrow pointing to the thing it's about. A callout is often the clearest way to comment on a particular word in a busy drawing.
Adding and editing a note
Choose Sticky note, then click where the note belongs. Its pop-up opens so you can type. To read or change it later, double-click the icon, or use Comment, Open or close its pop-up. Open all pop-ups and Close all pop-ups do the same for every note in the document.
An open pop-up shows the author, date, the words and any replies. Drag its title bar to move it, drag its corner to resize, and double-click the words to change them. A dashed line joins the pop-up to its note, so you can always see which note you're reading even when the pop-up has been moved aside.
Comment, Properties changes the colour, author and subject, which helps when several people are commenting.
Replies and status
Notes become a conversation once other people answer them. In the Comments panel you can reply to a note, set a status, tick a checkmark, change the text or colour, copy, lock or delete. Comment, Review history shows who set which status and when, which is useful on a document that goes back and forth a few times.
The panel also searches and filters, by kind, author or status, so you can show only the notes still open, or only those from one reviewer.
Sharing your notes
If the other person has the PDF already, you don't need to send the whole file again. Export your comments as XFDF or FDF and send that small file; they can import it into their copy. A summary PDF of the comments gives a readable list of everything you said.
If the notes should become part of the page, flatten the comments. Bear in mind that a sticky note's text is hidden in its pop-up, so flattening keeps the icon on the page; typed text is the better choice when the words must show in print.
Notes that work
Keep each note to one point. Three questions in one note get one answer. Put the note right beside the thing it's about, and say what you'd like done, not just what's wrong. Set your name for comments before you start so replies reach the right person.
PDF by Zaweba keeps all of this on your PC, so drafts and private papers stay private.