The best way to learn any kind of game design when you're starting out is to reverse engineer it, take the game, analyse it, break it down and understand it's logic, it's rules and how it works, and then recreate it.
It's a great process and you learn as well as teach yourself.
Let's look at Connect 4:
The aim of the game is to line up four objects either vertically, horizontally or diagonally; whilst stopping your opponent from doing the same.
Right off the bat I would start thinking about using Constructs built in physics behaviour, allowing the objects to sit on top of each other and fall realistically. For scoring I would use collision events, each counter could have four separate collision zones to track collisions with counters of the same colour; the winning conditions would likely be tracked by a dynamically altering variable, which would determine when a player had aligned four counters.
For simplicity, I would make the game two player, as programming an artificial opponent might be a much for a first try.