Following the War of 1812 the US and Britain shared somewhat frosty relations for a number of years (though war was never really likely again). What brought the nations together were shared economic interests. Britain needed raw materials from the US (wheat, cotton), whereas the US consumed British-made goods. Of course, commercial rivalries were also involved.

It's easy to forget that the US-Canadian border has not always been stable and that it was actually a source of contention between the US and Britain long after the War of 1812. A significant benefit here was the demilitarization of the Great Lakes region shortly following the war (1818), but the official border between the US and Canada was still contentious. Maine and New York were sites where border disputes actually jeopardized relations on numerous occasions. A lot of these incidents were rather small in the grand scheme (an American steamboat, the Caroline, was commandeered, an American killed by a Brit, etc) but they tapped into larger feelings of resentment on both sides. Americans were often frustrated that Britain didn't really respect American sovereignty or treat them as equals on the international stage. Britain worried about American interference in its imperial affairs (Canada, for example, rebelled in 1837 and a few Americans fanned the flames in attempts to spread the "spirit of 1776". Yeah, the British didn't like that).

Border disputes basically prevented these animosities from dying down naturally, but the US and Britain managed to hammer out diplomatic solutions to northern border issues which greatly contributed to the building of a more productive international relationship. The Webster-Ashburton Treaty of 1842 settled disputes over the US-Canadian border in the east (until Minnesota or so) and the Oregon Treaty of 1846 settled the western half.

Britain and the US also argued over the slave trade, which Britain abolished in 1833 and then put pressure on the US to join in. Southern Americans hesitated for fear that suppressing the African slave trade would lead to suppression of slavery altogether (remember that importing slaves to the US was made illegal, per the Constitution, in 1808). As such, the US refused to sign a number of anti-slave trade treaties. Consequently, a number of actual slave traders would fly US colors at sea. When the British started searching American ships to combat this, tensions between the two countries were strained.

By the time of the American Civil War, the two countries had built up a pretty strong framework for working out disputes diplomatically. While it's common to muse (on this sub and in general) about whether the British or French might have joined in the Civil War, actual involvement was never likely (that's a whole explanation on its own, I won't get into the details of the international side of the Civil War here). But it did create a few more disputes between the US and Britain over things like harboring Confederate ships and a (very) small territory dispute near modern-day Vancouver. Those disputes and others were resolved in the 1871 Treaty of Washington.

Basically, then, the US and Britain took decades to become close international partners, yes, but managed to cultivate a strong diplomatic relationship which prevented molehills from becoming mountains.

hi! not to discourage further discussion, but fyi, there are a few posts to get to started in the FAQ

• Anglo-American Relations

When the U.S. had the Confederate States, Britain traded a great deal with them. I'm talking cotton. As the industrial revolution took its toll further on the east U.S., trade flourished, which, as a result, helped a ton with foreign relations.

Let's also not forget that during this time, cultural similarities were extremely smiled upon. That definitely helped aswell.

To top it all off, we entered World War 1 as an ally to the British.