Identify the agents. An agent is any entity that makes a decision in the game. This includes any players of the game. If different states of the game occur with some probability, then chance is also a player.
Identify the decisions that the agents make. At each juncture in the game, make sure that you understand how many choices the decision-making agent has and the consequences of each.
Identify the payoffs. Some games have easily quantifiable payoffs, like monetary rewards. Some games have qualitative payoffs, like happiness or sadness. Assign values to qualitative payoffs that reflect their relative desirability.
Put the game in sequence.
Draw a dot to represent the first decision in the game. This dot is called a node. Write the name of the agent that makes the decision at this node next to the dot.
Draw a line off of the node to represent one possible choice of the agent. Repeat until you have one line for each option that the agent has at this juncture. Label each line with the choice that it represents.
Pick one of the lines from Step 2. If the choice leads to another choice, draw a dot to represent the next decision node. If the choice results in a payoff, write the value of the payoff at the end of the line. Repeat with each line.
Repeat Steps 1-3 for each node. Repeat this process until each path terminates in a payoff.
Connect the indistinct nodes with a dashed line if the agent making the decision at any node cannot tell whether he is at that node or another node. Nodes that cannot be distinguished from one another comprise a set of indistinct nodes.
Pick a node. This node will be the first decision in the subgame.
Trace the branches that come from this node all the way to the end of the game. This tree is a potential subgame.
See if the subtree includes any indistinct nodes. If it does not, it is a subgame. If it does, it is a subgame only if it includes the entire set of indistinct nodes. A subgame may not include a partial set of indistinct nodes.