Elections in the EU can be categorised into four levels:
European
National
Regional
Local
The European Electoral Office is the body which oversees and manages European elections only, however it may supervise all other elections in the Union to ensure they adhere to minimum standards set by the Parliament.
The Parliament is compelled by the Basic Law to regulate all elections in the Union to ensure freedom, fairness and to prevent corruption, however the majority of electoral regulation is reserved to the Member States.
Elections to the Parliament occur every 5 years in the months of April or June, unless early elections are called. There are 750 Members of the European Parliament (MEPs), half of which (375) are elected from unionwide lists, while the other half are elected from national lists.
Each voter casts one vote for a party. This vote is counted as a vote for both that parties national list and its unionwide list. The seats are then divided proportionally between the parties based on their respective voteshares at the national and unionwide levels. Unlike in systems used in Germany, Denmark etc. there are no levelling seats, meaning that the results of an election could still be somewhat unproportional.
The Parliament must elect a new Chancellor at its first meeting. Prior to the election, each party must nominate a leader, and if the party receives any seats, that leader is a candidate for Chancellor. Only these party leaders may be candidates. The Parliament then votes in successive rounds in which the candidate with the fewest votes is eliminated. This continues until either one candidate receives 376 votes, or there is only one remaining. That candidate is then considered elected Chancellor.
Every 5 years, a new president is elected for a single term. They may not serve more than one term. The President must be voted in by the parliment.