other 其他的(adj) Some students stayed in the classroom, and other stuents left.
the other 另一个(n)，只会出现在短语one...the other中，很好区分
There are two boys here. One is sleeping, the other is playing with toys.
another 另一个..（没有固定的数量）如：I have another apple. 我想再要一个苹果。
Others 其他的东西(n),跟other的区别就是other后面还要加名词，others本身就包含名词，有点像my和mine的形式。Some students stayed in the classroom, and
others left. (others=other students)
the others和others用法相同，关键看具体情形要不要用定冠词加以确定。
大家看呢？