Either means one or the other of two.

• There are roses on either side of the door.
• I don’t like either of them.

Neither means not one and not the other of two.

• I like neither of them.
• Neither of my brothers can sing.

Both either and neither are used to talk about two people or things. To refer to more than two people or things, any or none should be used.

• You can have either of the two shirts.
• You can have any of the three shirts.
• You can have none of the three shirts. (NOT … neither of the three shirts.)