Fritz for Fun 13: how do I add positions to a new database? My aim is to create a database of endgame positions taken from Van Perlo's Endgame Tactics in Fritz for Fun 13.

I've created a new database, but I do not know how to add games or positions. How do I add content to my empty database?
I'm not familiar with Fritz for Fun 13, but I have information about Fritz 13, which I will assume is the basis for your variant. 

I'll also assume that you want to add a game / position manually, rather than import one (or a collection) from, say, a PGN file.

New Game: You can enter the moves for a new game by simply setting the players to 2-player mode, instead of player vs Fritz.  If you can't figure out how to do that, turn on "Infinite Analysis" mode with Alt-F2. That will prevent Fritz from entering an engine move. Then, just enter the moves.

New Position: Choose the menu option "Insert, Position Setup". Then, clear the board (in Fritz 13, it is pre-populated with the start position), and drag-and-drop or click-click your way to populating the position. Hint: In Fritz 13, if you click the white piece in the legend, and then left click on a square, you get a white piece. If you right-click on a square, you get a black piece. So, you can save yourself about 30-40% of your setup clicks by just selecting white pieces.

Finally, specify the side to move, using the appropriate checkbox. If one of the kings is in check, of course, you cannot save the position until that side is specified as having the move.

You may have to specify castling rights (kingside and/or queenside) for either white or black or both, if the kings and rooks are in their original positions, but the setup wizard (dis-)allows that side's castling erroneously. However, the wizard settings are generally correct, in my experience.  Only when either the king or the rook have moved from their home squares and then returned to them will the wizard's settings be wrong.  Don't worry about the king being in check or any of the relevant castling squares being under attack; the move entry function will prevent an immediate castling attempt in that situation.

Then, confirm that you're done with the position setup using the Ok button. You will then have an open game window (but not a saved game).

Saving Games and Positions: The last step is simply to save the game/position. In Fritz 13, if you had clicked on a database (or had a list open) before you started the game/position entry process, that database would be where the game/position is saved by default if you use the "Save" menu item.  Otherwise, you have to navigate to the appropriate database using the "Save As..." menu option. So, I generally select my database first.

Tip: You can actually use a copy/paste operation to save the game from an open game window into a database. There are tons of ways to specify "copy", including right-clicking in the Notation pane, or by typing [Ctrl][C]. Once you've put the game in the clipboard (the results of this copy action are invisible, but trust me, it's there), you can paste it (any way you like) into a selected or open database, a Notepad window or other text editor, or an email as a text attachment.  But watch out; if you paste it into a database window, different versions of Fritz are inconsistent about whether a subsequent Replace operation will affect the pasted game.  To be safe, I close the open game window, and then open the game from the database list.  That ensures that a later Replace will put the game back in that slot.