Also see comments below from ainurakne on Unilang.org
So, you probably know that asking questions in Estonian can be quite easy. One way, which also exists in English, is to simply keep the structure of the question the same as with statements but but end with raising intonation.
Or in an advert for car rental in Tallinn that I saw on the train:
Vajad Tallinnas autot?
Need a car in Tallinn?
In the written language or in more formal speech you have learned that yes-no questions are prefaced with kas.
Kas oled valmis?
Are you ready? (Q you ready)
Kas vajad autot Tallinnas?
Do you need a car in Tallinn?
This you refers to the addressee, not the 'indefinite you' of many colloquial English sentences, which is referred to by one in more formal English.
Kas vajatakse autot Tallinnas?
Does one need a car in Tallinn?
However, the most colloquial way to ask a question in Estonian and a way that learners are advised to avoid because it can make you look un(der)educated or rude in the wrong situation is to end a statement with vä or ä.
Yesterday I heard a little girl ask her friend.
Lähed koju vä?
Going home? (you.go to.home Q)
This question maker should only be used in the spoken language and amongst family or friends. In other situations it is considered out of place.
You would ask a work-colleague that you are on friendly but professional terms:
Kas sa lähed koju?
Very often you will simply hear ä at the end or sometimes a sort of double question with kas at the beginning and ä at the end. The marker when unstressed allows the speaker to signal that they are somewhat unsure or hesitant, more so than a normal question or are maybe looking for the speaker to agree with their assertion.
Sina tegid seda kooki ä?
You made this cake?
It is kind of hard to explain this marker as you won't find any written rules in any grammar books. The best thing to do is listen for it in the speech of your Estonian friends (if you have any) and make a written or mental note of the question/ statement and the situation. If you replicate the speech of your peers you'll blend right in. Just make sure to also make a note of where they don't use it. That is also important to remember.
Comments by ainurakne:
I'm pretty sure it has evolved from 'või'(or) - at least I sometimes use 'või' that way, since 'vä' sounds so very childish.
I think it has evolved like this (I took your sentence, although I think it's not the best for this example):
'Kas sa lähed koju või mitte?' or maybe even 'Lähed (sa) koju või ei (lähe)?'
This has contracted to '(Kas sa) lähed koju või?'
And now some people use 'vä' instead of 'või': 'Lähed koju vä?'
But I haven't heard anyone use just 'ä' instead of 'vä', yet.
'Kas vajatakse autot Tallinnas?' - I think that adessive + 'on vaja' is used more often than the verb 'vajama': 'mul on vaja', 'sul on vaja', etc..., (actually allative (mulle on vaja), ablative (mult on vaja) and elative (must on vaja) forms exist also).
This can be transformed to passive very easily by omitting the person(or whatever is used) and just using 'on vaja', for example: 'Kas on vaja autot Tallinnas?' or 'Kas on autot vaja Tallinnas?'
Comments by iidala:
The origin of "vä" is deffinitely "või". But you may notice one interesting thing about "vä". The more educated and grown a person is, the less accent falls on the "word" "vä". Teenage girl asking: Mina VÄÄ? puts all the accent on VÄÄÄ???? Grown up in casual conversation asking "mina vä?" almost sounds like "MINA v?" or "MINA vah?"
Aitäh ainurakne ja iidala!