Explain the responsibilities of student council leadership to your students. They should know what being a leader entails and what they will have to do if they are elected.
Have your students nominate candidates for the election. Every candidate must have at least one other person nominate him or her for the election. If you are dealing with a particularly large number of students, you may want to require that two or more students nominate the same candidate.
Hold a campaign. Delay the actual election by one or two weeks. If you wish to turn this into a class project, you should delegate different responsibilities to different students. Have the students assemble campaign teams, and design posters to put up around the school or classroom.
Organize a student debate. The nature of this debate will depend on the responsibilities of your school's student council, but tell students to focus on issues that other students can relate to. Things such as school dances and class trips are often good topics. Have the student candidate stand at the front of the classroom. Other students can ask questions freely or write them down and submit them to you in advance. You may wish to act as moderator yourself if you want to keep control over the class, or pick a student to fulfill this role.
Put a box at the front of the class and hand out blank sheets of paper to all your students. Students can write their vote on the paper and put it in the box. You may need to do this during a break or after class. Count the votes and announce the winner to the class.