I would like to save my games AND favorite puzzles so that I can go through them. It seems like SCID could be good for this but I just cannot figure that program out. It is not easy to learn at all.

Any programs out there that would make this easy? Surely there is... I just don't know what to look for.

Its not as hard as you think. First thing you need to do is create and name a new database in the file menu. Then go the tools menu and select import one game. If you have the group pgn files merge program, then you can import an entire collection of games into the database. I dont know about puzzles though. I use it mainly for databasing.

Chessbase Light 2007 Premuim is pretty easy to use and not too expensive.

klc57690, Chessbase is easier to use but it costs money. A typical trade-off:  you have to decide whether to throw time or money at the problem!

Isn't it enough if you just save the pgn file (it is present in the corner or all these chess boards on chess.com) and open it other chess programs? Like say glchess on ubuntu or gnuchess?

I too wish things could be easier but I'm not sure they can.

As for people explaining here in two sentences, I don't think it helps unfortunately. It'll take more than two sentences to explain all things to a novice like me.

You could try downloading Winboard

http://www.tim-mann.org/xboard.html

Is free and I believe it has what you are looking for... 

For puzzles, I suggest you download PROBLEMISTE. It's tiny, but brilliant for mate in x moves. There are also collections of probably hundreds of thousands of problems to download, and it calculates all defenses,allows you to try moves and tells you what's wrong with them. you can search through you collection for different problem types, really easy to use. It handles problem better than any chess playing program I know. http://www.problemist.com/