Merhaba.

Is the letter "â " used in Turkish? If so, when? And what does it sound like?

  * This sign  [circumflex accent] used when it is necessary to  indicate long vowel [ long "a" in this case] in Arabic and Persian borrowings.

 * It is used to seperate the words which is written same but having different meanings. Such as ;

hala - aunt

Hâlâ - still,yet

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adet - number

Âdet - custom

[Aadet ]

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*  It is put on "a" and "u" letters if they followed by  light "g" and "k" sounds in some Arabic and Persian borrowings, such as ;

dergâh, gâvur, karargâh, tezgâh, yadigâr, Nigâr; dükkân, hikâye, kâfir, kâğıt, Hakkâri, Kâzım; gülgûn, merzengûş; mahkûm, mezkûr, sükûn, sükût

* If it is used for the purpose of  softening the sound , such as ;

kar = snow

Kâr = profit

then, you read  the consonant "K " softer.

Check this video about how the teacher reads  "â " [ at  1.14 minute ]

http://www.youtube.com/watch?v=T40k0SP_adk