There is not one single election to decide this as happens in parliamentary democracies such as the United Kingdom. In the United States, there are many different elections that decide which party will control each house of Congress.
The elections for the House of Representatives are fairly simple. Every two years, all of the seats are up for election. But each seat is decided in its own election. There is not one big election where people choose either the Democratic Party or the Republican Party. Instead, all 435 seats are decided in individual elections that generally include Republicans and Democrats but can also include people from other parties. Whichever party wins the majority of the individual elections will control the House.
In the Senate, things are a little more complicated. The Senate is controlled by whichever party holds the most seats. However, only one-third of these seats are up for election every two years. Each seat is only up for election every six years. So there is no one election that ever determines who will hold each seat in the Senate.
Of course, it is possible (as is the case today) that one party will control the Senate and one will control the House. In that case, no party can be said to control all of Congress.