The answer depends on your state of residence & registration.
All states allow for you to vote absentee (that is, by mail, and thus prior to election day) if you have a specific reason that is protected by law. The most common example of this is serving in the armed forces abroad. A few states allow anyone to request an absentee ballot for any reason, but this is uncommon. In all cases, you must register to receive an absentee ballot one to several months before election day (exact timing varies by state).
Some states allow for early voting, without the need to register as absentee. This is most often done through the mail, but is occasionally offered at the polling place. Voting early is a great way to secure your right to vote, especially if you think you might be unable to reach the polls on election day.
However, I believe the intent of the question is to ask: "what happens if I haven't done any special registration, and I happen to be sick/busy/tiedup on election day, and I miss going to the polls?" Unfortunately the answer to this question is: you're totally out of luck. If you have not voted by the time the polls close on election day, you have lost your right to vote - even if you had a really good excuse.
((Small caveat: if you are already standing in line waiting to vote, and then the polling place closes, you are guaranteed by law to be allowed to vote. However, no-one new will be allowed to get into that line.))
If you know that you can not be at the assigned poll on election day, you can vote in advance by absentee ballot. The details on how to get a ballot depend on the state. In some states you can cast your ballot early; in other states, you are given a ballot to mark and mail in.
You cast your vote at a polling place.
polls, polling is a survey process
Via absentee ballot, just like anyone else who is unable to vote at their designated polling place on election day.
The place would be called a polling station. In the polling station you would mark your ballot in a polling booth. You would then place the vote into a ballot box.
Make sure to check the location of your polling place before election day to ensure you know where to go to cast your vote.
It is a place where you cast your vote
You cast your vote in a voting booth, which is located at a polling place.
People vote at Polling Places
......polling station.
A precinct is a geographic political subdivision. A polling place, on the other hand, is simply a place where voters can go to vote. A polling place may be in a school, a community center, and so on.
Most states and municipalities offer "Absentee Ballots" to those who are otherwise unable to vote at designated polling places.There are also proxy and mailing voting systems.
Votes are cast a polling place. Depending on the type of voting equipment used, the votes may be cast at the voting place or at a central location. in the national [ presidential ] election votes are counted at each poll then city-wide tabulated at city Voter Registrar's office then sent to Secretary of state for state-wide validation