How do I connect my wireless headphones to my macbook air

Wireless head phones works on principle of wireless technology.
The phone has a reciver and tv or Audio system has a transmitter ,.
WiFi/blue tooth are examples.

Just take an audio cable with on one side a 3.5 mm (headphone) plug and on the other side 2 normal audio phono plugs.

Plug the 3.5 mm side in the headphone output of your MacBook and put the other side in one of the inputs of the Bose system.

try reseating the wireless card or airport card. if that doesnt work. turn off your wireless router and your macbook. leave off for 10 mins then turn on the router first then macbook. try to connect and see if that fixes the problem.

What I did to connect to BOSE wireless speaker to my MacBook air was go in advance settings and uncheck all three options there and then press the wireless button until it beeped--> then I was able to pair it to my laptop. Success!

The speakers should directly connect to the "line-out" socket on your Macbook computer, without any need for adapters.

I have _never_ seen a wireless router that had _any_ "audio" capability -- what you're asking for seems to be unreasonable.

Any "Dollar Store" or the "big-box" stores (such as Best Buy, Office Depot, Staples, Future Shop, Wal-Mart) should have adapter-cables.

You laptop may have sound prefs set to external speakers, or if there is a red light coming from the headphone jack. the mac thinks the headphones are still there.
Plug in and unplug the headphones an see if the red light goes out. may take a couple of times. Be gentle

The problem is that the headphone jack for you Macbook Air is a copy Analog (standard headphones) and Optical (toslink) jack. The jack has a small microswitch that detects when the cable inserted into the jack is a metal analog connector or a fiber optic toslink cable. The reason your seeing the "NOT ALLOWED" sign (circle with a slash through it) is because you cannot not adjust the volume on the sound when the output is in DIGITAL MODE. To verify this, drop down the jack cover on the side of your macbook air and place your index directly in-front of the headphone jack about 1/2" away from it. Is you finger glowing red? That's because the fiber optic LED is turned on and Mac OS X thinks that there is a toslink cable inserted into the jack.
This is a known hardware problem with that type of combo-jack and affects a lot of other Macbooks, as well.
If your Macbook Air is still covered by Apple Care, take it into an Apple store and have them replace the jack. I know this is a pain, but it is the correct answer.
If your Macbook Air is NO LONGER UNDER WARRANTY, you can attempt to fix this yourself, but be warned, you could break stuff!
Here is a thread at the Apple support forums discussing this issue: http://discussions.apple.com/thread.jspa?messageID=3255575
The above link is good background reading and will help you understand the issue further. The short answer is that many people have inserted a toothpick (other similarly sized NON METAL object) into the headphone jack, wiggled around until the microswitch is clicked off, then normal audio resumes. My 2009 Macbook Pro 17" has the same issue, but I have found that I can take a regular pair of headphones, insert the jack, wiggle it, remove it, reinsert, remove it....and repeat this process until the switch gets toggled. It's annoying, but I have to do this until I get home and can send it back to Apple for warranty work.

An alternative way is always try to repair it yourself. There are Mac Repair Guides that show how to open an Macbook. Watch out for the ribbon cables, those tear easily. Replacement parts are usually available on Ebay. There are third party services that can do it for you, like Mac Repair NYC.