How is the module Userpoints Donation intended to work? I enabled the Userpoints Donation module (part of Userpoints Contrib). Then I put a check in the settings for the type of material - (Choose which content types should show a donate points link).

What's next? Nothing has changed. It says "Only the checked content types will show a donate points link". But no reference appeared.
The purpose of the Userpoints Donation module is mentioned near the top of the module's source:


  ... uses User Points API to give users ability to give points to users.


But "give" actually means "transfer", as shown in userpoints_donation_giveform_submit(), which:


increments the amount of points for the user who receives the donation (= receiver).
reduces the same amount of points for the user who donates them(= donator).


Before actually doing so, various extra validations are performed, such as:


Does the donator have sufficient points, so that after transferring the points the user points balance of the donator is still positive?).
The receiver has to be a valid user.
You cannot transfer points to yourself.
The amount of points donated cannot be below 1 user point (which also implies that the donator can only "give" points, not "take" points ...).
...


However, for an appropriate link (with title "Donate points to this user") to be shown to the user who wants to do such donation, it is required that such user has been granted the permission "give points to another user". So if "Nothing has changed" (as in your question), it could well be that the required permission has not been granted yet.