I want to run the following query:
select the number of men and women who voted for each party in each US state. Can this be done in a single query? If so, whats the best way to approach it? Nested selects?

Depends on your database schema of course, but generally you should be able to GROUP BY party, selecting COUNT(*), to get your list of totals.

Using latest Wamp server, MyIsam engine. I was thinking of doing a main select on the party, then seperate select queries for each count or is there a more efficient approach?
Basically the results will be in this format:
party male female state

Code:

SELECT party, SUM(IF(gender=Male,1,0)) male, SUM(IF(gender=Female,1,0)) female, state FROM results GROUP BY party, state;

I tried your solution Wojjie as is in mysql console and it gave me unknown column Male. I tried it again with the Male and Female comparisons in single quotes, i.e Gender='Male' and Gender='Female' and it worked.
One odd thing of note, I tried this query in phpmyadmin and it failed. This worked though, same output as mysql console
SELECT party, SUM(gender='Male'))as Male, SUM(gender='Female')) as Female, state FROM results GROUP BY party, state;

Thanks again.

Your welcome, my example was more meant to be written in "english" not really meant to be used directly with SQL, but I am glad you managed to get it working.