Choose the criterion on which the polls are to be investigated. This criterion, no matter what meaning, needs to be a proportion. For example, if the polls are asking college students about plans for graduate school and you are interested in determining whether the responses of the two polls correspond in terms of the affirmative (e.g. "I plan to go to graduate school"), then your criterion of interest is the proportion of students who say yes.
Find the number of responses for each poll. Many polls are not explicit about stating how many responses were received. In this case, the poll should have a footnote stating a number in the form of something like "n = 1022." In statistical studies, "n" refers to the number of subjects. Thus, you should interpret such a footnote as the poll having 1022 responses. Call the number of responses for the first poll "n1" and that of the second poll "n2."
Subtract the proportion of one poll from that of the other. Call the first proportion "p1" and the second "p2." The difference of proportions is then "p1 -- p2." Call this resulting number "numer."
Find the combined proportion. The equation for combined proportion, "pc," is given by "(n1*p1 + n2*p2)/(n1 + n2)."
Multiply the combined proportion by one minus the combine proportion. Call this "pt." In terms of a formula, "pt = pc*(1 -- pc)."
Multiply "pt" by the sum of the inverses of the number of responses for the two polls. Call this number "pr." As a formula, "pr = pt*(n1^-1 + n2^-1)."
Take the square root of "pr" and call it "denom."
Divide "numer" by "denom." This is the Z-score for the test of proportions.
Compare the Z-score to the values in a Z-table. You can find a Z-table in any introductory or applied statistics textbook. The value in the table most closely associated with your Z-score will have a p-value associated with it. This p-value is the statistical significance for the two polls.