I have read there are 3 types of stages in checkers, i.e. opening, mid and end game. I am confused on how to determine when these three stages exist on the checkerboard. For example, how do I tell when the game is at the mid-game stage, is there a certain board layout or board configuration that allows me to ascertain the stage of the board?
There are very few specific board setups that detail early- mid- and late-games. It might be easiest to keep track of which stage you are in based on how many pieces and how many kings each player has and comparing to one another.
For instance, when very few pieces remain on either side, regardless of ratio of kings, this can be assumed to be the late game. Another example of late game is when one player is being dominated and has about one-third to one-half of the pieces that the other player has.
In the early-game, as another answer mentioned, some combinations are easy to memorize, especially if you play a lot. In the late game, some strong finishes are to be known in general, such as having all enemy pieces in a position where none of them can move (e.g. have your pieces block off your rear end) or sweeping the board with kings.
Mid-stage is more or less defined as the messy stage, where you're making up every move as you go and taking time to decide based on how you think the other player will react and how far ahead you can plan, aiming for the late stage. The two sides are approximately even and players are vying for the most profitable positions.
From what I know, this partition is like in Chess, the opening stage can be memorized, the end game has a lot of skill involved and can be learned in lessons, the midgame is all that in between. To the best of my knowladge there is no formal defenition of this 3-stages partition, such that any state of the game can be classified to one of them.
Opening, Mid-Game, and End-Game:
It is convenient for study purposes to divide the game into three phases; opening, mid-game, end-game. This division is not entirely artificial as the chief motives underlying each phase are really very distinctive. The dominant theme of the opening may be said to be preparation for the battle which rages throughout the mid-game; the conflict of the mid-game is resolved in the end-game. In this latter we seek to prove the real value of the seeming advantages gained or lost during the earlier play.
One need only define the purpose of the end-game to see that this must be the most vital phase of the game. The preceding phases are concerned with creating good prospects, in the end-game we consider the actual result, win, lose, or draw. A slip at this stage and all the brilliant ideas of the past become worthless. On the other hand it is the end-game, demanding as it does both precision and artistry, that may give one the chance to recover from a weak position and turn defeat into victory. In draughts the best player wins and the proof is here - in the end-game.