First of all, I'd like to point out that in British pronunciation, both
/ˈaɪðə(r)/ and /ˈiːðə(r)/ are acceptable. The US tend to use the latter version.
Either usually means 'one or the other':
Either you choose me, or her. You can't have both!
The reason why a lot of people have doubts over whether either...or... carries a singular or plural verb is very simple - both are acceptable! The same goes for neither ...or...
Having said that, however, a singular verb is more common, and is certainly preferred in formal usage.
Which restaurant shall we go to?
Either Fuji or The Golden Lotus is fine. I like the sushi in Fuji, but I prefer the duck in the Golden Lotus.
Do either of you know how to get there?
Can you believe that neither my father nor my mother drive?
I wasted my journey. Neither James nor Melanie was in.
Or buy from Amazon.com