This is similar to the traditional Ncaa March Madness Bracket pool.
Print out the tournament bracket from above, estimate the total number of people you think will be interested in entering the pool and print that many brackets.
Pass the printed brackets out to friends, family, and co-workers. Each person is to fill in the bracket with the team they think will win each series. For a tie breaker have each person write down what they think the total number of runs scored in the final game of the World Series, or you can use your own idea like total points scored for the entire World Series.
Collect the filled out brackets, if you want to do a little extra for the participants, print every person in the pool a copy of every other person's bracket. This is a lot of printing but ensures to all people that the pool is being run fairly.
Each series of each round is worth a set number of points, you can determine this on your own, but be sure to let all of the entries know before the tournament begins what the scoring system will be. We prefer to do semifinals 1 point, league finals 3 points, and championship 5 points. After the championship game calculate the total number of points by each player. The person with the most points is the winner or you can set it up to pay more than one place in accordance to how many players entered.
*Please check your local gambling laws for information on the legality of wagering money on office pools.