The parliament of the people, the peoples voice in EU. 766 members in total at the moment, going down to 751 members after next election. All 28 countries have separate elections with a number of representatives corresponding to size, population and what they have been able to leverage in the negotiations of the council. Members are elected for 5 years and we are coming up on next elections!
The parliamentarians are arranged into 7 different political groups (for now) and several independent representatives who are not accepted into the groups and/or do not want to participate in them.
The responsibilities of the parliament are:
1. To pass legislation in cooperation with the councils.
2. To supervise the EU institutions - mostly the commission. The parliament has the authority to approve or reject the commissions president and the authority to approve or reject the proposed commission as a whole (They cannot reject the individual nominees/commissioners).
3. Has a joint responsibility over the budget of EU
The parliament has a president who is elected for a 2½ year period. For now Martin Schultz resides. The presidents role is as a representative for the parliament and the leader of plenary meetings.
The process in the parliament is conducted by all parliamentarians divided inte committees with the responsibility to review legislation and by majority vote, write a recommendation of what the parliament should mean about issues and legislation coming to a plenary vote. Legislation has to pass inspection from relevant committees before getting up for a plenary vote.
The plenary is all the members of parliament meeting to debate issues. A lot of it is a question of voting on items on the agenda after they have gotten a recommandation from the committees.
Sources
http://ec.europa.eu/prelex/apcnet.cfm?CL=en
http://www.europarl.europa.eu/sides/getLastRules.do?language=EN&reference=TOC#T2R2