What were three major components of the "American System" under John Quincy Adams?

I assume that you are asking about the economic policy that was promoted by people like Henry Clay and, before him, Alexander Hamilton.  This was a policy that was meant to create the sort of national economy based in part on manufacturing that these leaders preferred to have.  There were three main aspects of the American System.  These were a tariff, a national bank, and federal subsidies for “internal improvements.”

Let us look at each of these in turn.  A tariff was something that leaders wanted because they felt it would promote American manufacturing.  It would increase the prices of imported goods, making it easier for domestic goods to sell.  The national bank was meant to create a stable currency.  It would issue money that would not lose its value.  This would make business more predictable in the US.  Finally, “internal improvements” were meant to improve the ability of people to trade within the US.  These improvements were to the country’s transportation system.  The point was to make things like better roads to promote the movement of goods from place to place.

With these three components, Clay and others like him hoped to create a stronger national economy.

What were the main elements of John Quincy Adams's American System?

The term “American System” is typically used to refer to a particular economic plan for how the US was to develop.  The plan is most closely identified with Henry Clay and is similar to what Alexander Hamilton proposed in the early days of the independent United States.

The American System proposed by Clay had three main elements.  These elements were to work together to advance American economic prosperity.  The elements were a national bank, a protective tariff, and a program of internal improvements.

The national bank was meant to put the country on a firm financial footing.  It would ensure that the US currency would be sound and that banks would not lend excessively and in risky ways.  The protective tariff was meant to make it easier for American manufacturing to get started.  The tariff would make imported goods more expensive, thus making it easier for American goods to sell.  Finally, the internal improvements would make commerce within the US easier.  Internal improvements were things like good roads and canals.  This would make it easier to transport goods from place to place.

Clay and others felt that these elements could combine to help the US economy develop.