These words are often confused by students.  Here’s an explanation to help you.

Another is used when there is more than one other.
Another means “one of many others.”
It can be a noun or an adjective and it is followed by a singular noun.

Examples:
One shade of blue is called navy blue, and another is called sky blue.
(…and another shade of blue is called sky blue.)
[There are many other shades of blue.]

This path takes you through the park.  Another takes you to the zoo.
(Another path takes you to the zoo.)
[There are many other paths.]

A customer in the store was on his cell phone.  Another was buying gum.
(Another customer was buying gum.)
[There are many other customers in the store.]

Other is always an adjective and can modify plural nouns or non-count nouns.
Other means “one that is different than this one.”

Examples:
There are other reasons I wanted to talk to you.
[I’ve already told you one reason and now I’ll tell you more reasons]

That’s probably true for other people but not for me.
[It’s true for people who are not me.]

There is other furniture that would look better in this room.
[This furniture doesn’t look good.]

No other is an adjective and means “this is the only one” or “these are the only ones.”
It can modify a singular noun, a plural noun or a non-count noun.

Examples:
There’s no other way to get downtown at this hour.
[This way is the only way to get downtown.]

There are no other possibilities I can think of.
[You can only think of these possibilities.]

There’s no other water for miles.
[This is the only water in this area.]

No other can also be used as a noun.

Example:
I love only you.  There’s no other.
[There’s no other person that I love.]

Others is a noun and is used to replace other + plural noun.
It’s used when there are many others.

Examples:
Although some people know what they want to do, others have no idea.
(…, other people have no idea)

Some excuses are believable, but others are not.
(…, but other excuses are not.)

A few of the exercises were easy, but others were impossible.
(…, but other exercises were impossible.)

The other is an adjective or a noun and is used when there is only one other.

Examples:
One brother is a lawyer, and the other is a doctor.
(…, and the other brother is a doctor.)
[There are only 2 brothers.]

One team played very well, but the other played poorly.
(…, but the other team played poorly.
[There are only 2 teams.]

One path led up the mountain, and the other led to the village.
(…, and the other path led to the village.)
[There are only 2 paths.]

The others is a noun and means all the other ones.

Examples:
Most of the lights on the tree were blue.  The others were green and yellow.
(The other lights were green and yellow.)
[The tree had three different colors – blue, green and yellow]

Half the cupcakes had white icing, and the others had pink icing.
(…, and the other cupcakes had pink icing.

I wanted to leave, but the others wanted to stay longer.
(…, but the other people wanted to stay longer.