Sticky notes do what the paper ones do: hold the thing you will otherwise forget, in front of you, until it stops mattering.
Using them
Add a sticky note, type into it, and it saves as you go. Drag it where you want it. Give it one of five colors: yellow, green, teal, blue or purple. Minimize one you want to keep but not read, expand it again when you do, and delete it when it is finished.
There is a cap on how many you can pin at once. Hit it and Basecamp tells you the number rather than silently refusing. Delete the ones that are no longer true to make room.
Color them consistently
Five colors are only useful if each one means something. Pick a scheme and keep it: one color for this week, one for admin, one for things waiting on somebody else. If every note is yellow, the color tells you nothing. Position works the same way. A note stays where you drag it, so the top of the workspace can hold this week's work and the bottom can hold what you are waiting on.
Private to you
Sticky notes belong to your workspace. No client sees them, and they are not attached to anybody's profile.
That privacy makes them tempting for the wrong thing. Coaching notes about a person drift toward health details and personal circumstances, and a sticky note is not the place for those. Information about a client belongs in the record for that client. That record is governed, it can be exported if they ask, and it can be deleted if they leave.
Client context goes in their notes field. The sticky note is for "order new tape measure" and "reprogram block 3 before Friday". A useful test: if the note names a client, it is in the wrong place.
If they will not load or save
Basecamp tells you when a note could not load or could not save, rather than letting it vanish silently. Both are usually connection problems. Do not treat a sticky note as the only copy of anything that matters.