Well the first step to doing UML is to first identify any objects you have. These will appear as boxes and will have properties and actions with them. Second you will identify what they call "actors" or people who interact with these objects. These usually appear as little stick figure guys. In Connect 4 there are two players but as far as the system is concerned there is only one actor, the current player.
Some objects you might have would be... board (where pieces are going to be contained), piece (the actual colored piece that you will place in the board) and Game which would keep track of things like who's turn it is, the player's color, who won and lost and would contain the current board setup and game restart.
Once you have identified the objects and actors, you try to fill in the responsibilities of each object and, as I have already helped you do above, identify the properties and methods of each object and how they interact with one another. Obviously the game object is going to handle the creation of a new board object, the board will interact with pieces as well as their position in the board, might have a function to check if someone created 4 in a row etc.
Read up on the game and you can quickly see how these objects might work with one another. Be mindful of all the objects in the game and the actions each object might take when working with the other objects. These are going to form your relationships in the UML diagram.
Below is an example of a UML diagram. Your's should be around the same size or so. Notice how the order object interacts with a client and an order string object. Also notice how the client has been inherited down into two types of clients. You could inherit down into a red and a black piece from "piece" but I think you won't have to as long as you make a property of piece called "color".
UML Class Diagram exampleAnother example which is a bit more complex shows actors and such...
UML Diagram with actors and a bit more complex scheme (Yours should be no where near this complex... this UML is for a Portal system)
Hope this helps give you an idea of what it should look like.
"At DIC we be UML mastering code ninjas... we also mastered gantt charts, timelines, and women. Ok I lied about the last one."