I played a very interesting game today, and I entered it in ChessBase reader, along with some comments. I would love to save this game in a database (.cbh) or as a .pgn, but I don't know how. Can you please help me?
It's not possible, in fact in "Chessbase reader", there is the word reader which means you can only pgn (or .cbh ...)
If you want to do such thing, my advice is for you to get a copy of the most used software like Chessbase or Fritz. Probably there is some free stuff which are doing the same but I don't know it.
I would recommend ChessDB which claims to be the best free chess database program out there, although that was in 2007 ;-). It is quite powerful for a free program with the ability to download from TWIC from within the program. Also import from a player's ICC history. You can hook up to UCI interface games engines.
Of course you can save your games into a database but you cannot import Chessbase format. It has good search capabilities for a free program like player reports and search for games with exact position match.
While you cannot save new games with chessbase reader, you can edit and replace existing ones. So what I do is open a .pgn file (I created one and copy and rename it for each tournament) full of empty games and edit these, i.e. double click an empty game, enter the moves and comments, then right click the game in the list and select replace which lets you edit the metadata and writes the game to the .pgn file. Only the site tag seems to be unavailable, but if you edit it manually, cb reader will display it if the tournament name is short enough.