The quick and dirty answer is that he essentially crossed both parties.

 

We'll start in the 1820s when national politics was ruled by one party, the Democratic-Republicans. Tyler began his political career as a member of this party as Governor of Virginia. In the fallout of the 1824 election between Jackson and Adams the party imploded, giving rise to the first two party system the nation had seen since the collapse of the Federalists in the early 1800s. On one side stood what would come to be the Democrats under Jackson. On the other stood what would come to be the National Republicans (later Whigs) with Adams. Tyler was appointed as a senator from Virginia in 1827 and joined the Democratic faction. However, while he was a Democrat in name, he disliked many aspects of the party as it was being run by Jackson and eventually split with them in the wake of the Nullification Crisis in 1832. I'm not going into detail on the Nullification Crisis because it would be a long answer that distracts from what was going on with Tyler. What you really need to know about it is that Tyler's actions of opposing Andrew Jackson made him a pariah in the Democratic Party. Jackson and his supporters held major grudges against all their opponents and Tyler had made the short list. Tyler eventually resigned from the senate in 1836 rather than be forced to violate his constitutional beliefs by the Democratic controlled VA State Legislature.

 

Tyler drifted towards the Whig Party and by 1840 was the party's nominee for Vice President running with with William Henry Harrison. Harrison, a nationally known war hero, was the key to the ticket and not much attention was paid to Tyler. It was generally believed he was attached to the ticket to help win Southern states. Whatever the reason, no Vice President had ever become President at that point so there was little reason to worry about Tyler in the first place. Unfortunately for the Whigs, Harrison died from pneumonia just one month after taking office. Tyler immediately declared the Constitution gave him full presidential powers and had himself sworn in as President, setting the precedent that eventually became the 25th Amendment. He essentially fell backwards into becoming the president for almost a full term. While Tyler initially supported the aims of the Whig Party, he soon broke with them on issues such as reestablishing the national bank. He twice vetoed legislation to reestablish the national bank. The Whig Party was furious, as national banking was an extremely important issue to them. The national bank was a battle they had repeatedly lost with Jackson and his successor Van Buren. Now that they finally had a "Whig" President, they figured they would be able to get it done. Tyler said no. His entire Whig cabinet (except Sec. of State Daniel Webster who was overseeing a treaty) resigned and the congressional branch of the party expelled him from the Whig Party. Led by the Whigs, Congress even began the first impeachment proceedings on a US President, however he was never actually impeached. Through all this Tyler would not resign his post and even tried to run again in 1844. However, being despised by the Whigs and distrusted by the Democrats he eventually withdrew and threw his support behind James K. Polk.