I have now been a US citizen for just over a week, and had a chance to prepare for the upcoming Nov 7 election. How different it is from where I was born! I was speaking about this to my wife, who spoke to a friend, who asked if I could describe the way voting works there... so here goes.
In Israel, we basically have general elections every four years - well, assuming that the government survives for that long, which I believe hasn't happened in close to two decades. But that's about it. There are usually between 25 and 35 parties to vote for, each of them vying for control of some of 120 seats in parliament (Knesset). While Israel tried the idea of voting separately for the prime minister, it had gone back to its traditional method, in which the leader of the largest party ends up the prime minister (although the process does not have to end this way, see below).
Each party presents an ordered "candidate list", providing the names of party members to the voters in the order in which they will fill won parliament seats. Number one on the list is the party leader, who is also the party's proposed prime minister. Some parties hold primaries prior to the election to form the list, although the smaller parties generally do not. Votes must be cast in Israel (no absentee ballots), except for navy men and employees for consulates and embassies abroad. This may sound surprising, but many Israeli citizens fly to Israel (at their own expense) to fulfill their civic duty and cast their votes on election day.
Each party offers a platform, and they can focus on pretty much any issue; some small parties get voted into parliament on single-issue platforms, such as the promotion of of the legalization of Cannabis (Marijuana). Only three platform elements can disqualify a party from being elected: negation of the existence of Israel, its democratic nature, or an incitement to racism. Otherwise, anything goes, if you can get enough people to vote for it.
At the end of the election, the total number of votes cast is divided by 120 to determine how many votes "represent" a seat. However, a party must gain a minimum of 2% of the total number of votes cast in order to "qualify" for a parliament seat, and that minimum number is higher than those necessary for a single seat, the intent being to reduce the number of parties eventually represented in parliament. Note that this number is higher than the number needed for one seat. With an average of about 65% turnout, and based on current population, one can expect around 3.2M votes to be cast resulting in about 26,000 "votes per seat".
It is possible and common to have "overage" agreements, where two parties agree in advance that one of them will "hand over" their excess or surplus votes beyond the last seat they won to the other party, who then gets to add them to their tally. The idea is that two parties that have a similar ideology can this way extract one more seat between them by adding their surplus together. Usually this type of agreement has some payback in the eventual coalition, and thus normally occurs between a small party and a large one. However, small parties occasionally band together to try and gain a single seat if none of them cross the qualification threshold.
If such an agreement does not exist, excess votes get redistributed between parties based on their proportional size resulting from the election; this is a little complicated, but provides a bit of additional excitement following the election as things are figured out and some parties may end up gaining or losing representation at the last moment.
Parties get financing based on a rather complex formula which takes into account previous parliament seats won as well as those won in the current election. New parties receive funding retroactively. Contributions are limited according to another formula which is tied to the consumer price index.
Once the election is finished and seats assigned, the president assigns the task of forming the government to an elected member of parliament. For the most part, this is the leader of the largest party. However, in the case where another block seems to have been formed which includes more than 60 members of parliament (a majority), the president may assign this task to the leader of the party heading that block. In other words, winning the largest block of seats in the general election does not guarantee a party the right to form the government. The president figures this out based on the recommendations of the leaders of all parties elected to parliament.
Once a member of parliament has been assigned the task of forming the government, they have 42 days to finalize it. If a coalition cannot be formed, the president then assigns the task to another member (usually from the opposite large party), who then has 28 days to form their government. While there are provisions for what happens if they fail as well, this has never happened. The process of forming the coalition government is complicated and delicate, requiring significant negotiation skills and political acumen, and must result in a block of 61 seats or more to represent a majority of voters. It provides much merriment to the media, and tends to sully the new government before it even takes office. Small parties often hold disproportionate power in this process, since they may swing the eventual government one way or another, depending on which of the largest two parties they side with.
And that's about it. We don't vote on specific issues, although a special referendum may be called (an extremely rare occurrence). Once we vote in the general election, all decisions are further made by the elected officials. There are no propositions, which is unfortunate; I find the notion of voting for major elements of public policy to be a great boon for democracy.