In Jackson's first term he negotiated a treaty with a few Cherokee to take their land. However, these Cherokee were not the legal government of the Cherokee and many Cherokee resisted, but they were forced to what is now Oklahoma by the Federal government over time.
2nd Bank of the United States
The 2nd Bank's charter which had been due to expire in 1836 had been renewed by President John Quincy Adams just before Jackson had been elected. However, Jackson, an opponent of the bank instructed his Secretary of the Treasury to stop depositing money in the bank and to withdraw all federal funds, but its charter was not set to expire again until 1856 and Jackson did not have the support in Congress to pass a bill repealing the bank's federal charter. While still chartered as a national bank the bank's business consisted entirely of private transactions from 1833 to its bankruptcy in 1841 when Congress agreed to uncharter it since there was no point in a bankrupt institution holding a federal charter.
Nullification Crisis Resolved
Andrew Jackson signed the Compromise Tariff, which lowered the high tariffs started under President John Q Adams and the Force Act which authorized the military to collect federal tariffs. South Carolina withdrew its nullification law, which made the Force Act moot.
Arkansas was about to be admitted as a state in 1836. Congress refused to grant it on the grounds that it would add another slave state. Michigan was also being considered at the time, so they decided to make them states in one bill. However, Congress would not pass the bill without the stipulation that slavery would not be allowed in territories south of the northern border of Arkansas. This is agreed and Arkansas and Michigan become states.
Andrew Jackson easily defeated Henry Clay in 1836.
Panic of 1837
Andrew Jackson had required that all federal land sales be paid in specie (gold and silver), which lead to a short depression. Andrew Jackson created the independent treasury and undid the specie requirement and the economy began to turn around.
1st Mexican-American War
When the Republic of Texas asked Andrew Jackson if he would annex it Andrew Jackson signed the treaty. However, Congress rejected it. Jackson convinced his allies to start a joint resolution including the annexation of Texas. This passed, because since it wasn't a treaty it didn't need 2/3s of the houses. Texas was admitted as a state. Mexico declared war. The war ended in 1839 with Texas ceded to the United States along with the southwest of the United States.
Martin Van Buren Resigns
Andrew Jackson's vice president Martin Van Buren disagrees with the Mexican-American War and sees it as helping the cause of slavery. He resigns.
2nd Mexican-American War
The Republic of the Rio Grande declared its independence in 1840 and asked the United States government for assistance. Jackson agreed to back it up on the condition that it would be annexed to the United States. They agreed and a treaty was signed. The Republic of the Yucatan also came to a similar treaty. The war lasted only shortly after Jackson's election to his third term as president, and historians think Mexico was counting on the Whig Party to win and to agree to end the war retaining the ante bellum status. The treaty signed recognized that the states of Rio Grande and Yucatan were part of the United States along with a small amount of land in the southwest (the Gadsen Purchase in OTL).