A basic way of looking at client sided and server sided hacks is that whenever you play a game, you as the client interact with the server. Whenever you send a command [or packet] to the server, it will reply with another command/packet/whatever word you need to understand the concept.
Clientsided: only you as the client can see this. For example lets say you created a program that can alter the graphics in the game. This would be consider clientsided because you will be the only one to see such alterations
Serversided: on the other hand, things like how much gold you have, your stat points, and even your combo hits are stored on a serverside. Even if you altered your gold value to 99999999, the server will still see what you really have and therefore your gold would not work.
More info :
And the first step to 'hacking' a game is OFTEN if not ALWAYS to start with leeching. When you look at other people's works such as the vac hack or teleport hacks you should be thinking 'whats going on' instead of 'why cant you make me gold hack?'
Once you develop a basic understanding, it's time to understand memory editing. This may be enlightening
