Japan and Manchuria
Japan had been longing to expand their empire, and found the perfect oppourtunity to do so when a Japan owned railway was destroyed in Manchuria (China). The railway was ran by the Japanese army, and when it was destroyed in 1932, Japan accused China of sabotaging it.
This influenced the Japanese army to take over Manchuria by force, and set up a "puppet" governnment there. They even renamed Manchuria and called it Manchukuo.
China appealed to the league. Japan told the league that they hadn't been aggressive, and were acting in self-defense to keep peace with China.
It took the year over a year to asses the situation, which gave Japan enough time to advance more in Manchuria. The league had no army to send in to control the situation, and without the support of America, their sanctions were ignored. Japan was a leading member of the league and so the league had to tread carefuly with the situation.
This event showed how powerless the league was. Britain and France were focused on keeping good relations with Japan. The event showed that the league was useless for dealing with strong nations, and dictators like Mussolini and Hitler took notice of this.
Italy and Abyssinia
Mussolini took notice of the leagues lack of action with the Manchuria incident and decided to make a move on expaning their empire in East Africa.
Italy sent their troops to Abyssinia (now Ethiopia) to conquer. The leaders of Abyssinia appealed to the league, and all that the league did was ban arms sales, which enede up being worse for Abyssinia than Italy.
This situation relied on Britain and France to take the lead and put pressure on Italy (with their own armies). However, Britain and France were reluctant to do so because they wanted an ally to work with them against Hitler. This event showed that Britain and France were more willing to work on their own interests, rather than the interests of the League.
Italy eventually left the league and continued to conqueer all of Abyssinia.
The Disarmament Conference
At this conference the League was supposed to decide on whether all countries should disarm as much as Germany were made to.
France was fearful of any kind of attack from Germany, and was unwilling to agree to any limitation to their armed forces.
Adolf Hitler said that if the world wasn't made to disarm on the same level of Germany, his country should have the right to rearm.
The League failed to make an agreement here, and so Germany left the LoN and started to rearm.
Reasons for the Failures of the League
French and British self interest
Absent powers (America)
Lack of armed forces
REached decisions too slowly