A brief, high-level overview:

Who were Japan fighting against?

Japan had been fighting the Republic of China since 1937 (although there were several skirmishes since the 1920s prior to then). In December 1941, they invaded British and Dutch territories in South East Asia (Malaya, Indonesia, Burma), the US Philippines, and several US islands in the Central Pacific, among others. They had previously been at war with the Soviets (which was a low-intensity border skirmish in 1938) and had occupied French Indochina in 1940 (modern day Vietnam).

What were they trying to do?

The Japanese had gotten into a war with China for a variety of reasons which are rather complex to detail but most immediately had to deal with a border skirmish at the Marco Polo Bridge in Northern China. The Japanese had occupied Manchuria in 1931 as part of the Mukden Incident and border clashes there were frequent. One such clash rapidly escalated into full-blown war. Despite some initial Japanese successes, the Chinese had inflicted heavy casualties on the Japanese and had managed to relocate much of their war industries deep into China's interior, making it impossible for Japan to force China to terms. Growing Japanese actions in China led to an embargo of vital war materials to Japan, and Japan's military, geared for a short war, would be unable to pursue the war to a victorious conclusion without access to these resources.

To solve this problem, Japanese high command deliberated and elected to "strike south" into the Dutch East Indies, which they referred to as the "Southern Resource Area." The DEI was very wealthy and had important war goods like fuel and rubber as well as rare earth minerals. However, the Dutch colonies were under British (and Commonwealth) protection, meaning that the Japanese needed to destroy the British positions in Malaya, Hong Kong, and Burma as well. In turn, the US in the Philippines posed a potential threat to Japan's supply lines to the south, so the Japanese chose to preempt it by attacking the Philippines as well. Admiral Yamamoto took this further and chose to attack the US battleship fleet at Pearl Harbor.

The war plan was to seize the core resource areas and then establish a defensive perimeter in the Pacific, building air bases on many islands. The idea was that when the Allied navies regrouped for a counter offensive, the Allied material advantage would be negated by the Japanese air bases in conjunction with Japan's fleet. Then, in a decisive naval battle, the theoretically qualitatively superior Japanese fleet would smash that of the Allies, resulting in heavy casualties such that the Allies would look to reach a negotiated settlement.

Did they have any allies?

The Japanese were allied to Germany and Italy (although their assistance was rather limited) via the Tripartite Pact of 1940. They also had an alliance with the Kingdom of Siam (although this was definitively Japanese-sided) and several puppet countries in China (Manchukuo, Mengkekuo, and the Reorganized National Government of China).

How well did they do?

Pretty poorly. While initial Japanese successes were well beyond the Japanese expectations, this was primarily due to deficiencies in the Allied defenses in the Pacific. The Japanese battle plan was fatally flawed due to a combination of poor Japanese logistical capacity as well as an assumption that the Allies would do exactly what they want them to do (which they didn't). Intelligence failures and poor cooperation between the Japanese army and navy compounded these flaws leading to decisive defeats such as in Guadalcanal and at Midway. The Americans, with a massive industrial capacity, were able to force the Japanese into a war of attrition, grinding the Japanese forces down and attritioning their irreplaceable elite personnel. American submarines waged a vicious campaign against Japan's already overstretched logistical system, crippling Japan's ability to make war. Eventually, the Americans, with both a qualitative and quantitative advantage, were able to commence a strategic bombing campaign that eventually rendered Japan's economic situation in peril. A combination of the atomic bombs, massive fomenting civil unrest, and a Soviet attack on Manchuria in 1945 forced the Japanese to surrender.