There's a guide for this online: MacBook Air 13" Late 2010 AirPort/Bluetooth Card Replacement iFixit keeps deleting my helpful comments on this as spam for no apparent reason so I will simply say: you need MHF4 antenna extensions.

This guide is helpful but doesn’t include the most important part, which is re-connecting the antennas. I’ve done this exact replacement in my mid-2010 13” MBA, and you will need antenna extenders (MHF4 female to male) to make it work. Other discussions on this suggest breaking off the antenna cable bracket near the hinge to get extra length, but that still won’t work. You need extensions. I found mine on eBay US, despite living in Canada - they didn’t appear on my local site for whatever reason.

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Also, be VERY careful when disconnecting the MHF4 connectors from the card (step 4). They’re rated for 30 disconnects max (I had to do a lot of research to find the right connector) and I managed to break one. I essentially had to tape the socket together once I got the extensions in the mail - just buy them from the beginning so you don’t mess around with trying to lengthen to cord like I did. That’s what caused all my issues.

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The exact item I bought was “2pcs MHF4 Male to MHF4 Cable Antenna Extension Female.”