I'm using 10.7 and my wife is using 10.8. I found the following (different) instructions from a thoughtful amazon reviewer for a simple way to set up wifi connection with the 2270dw. These instructions worked on both of our laptops:
As with so many tech units, it's the setup that is the hassle. I am a Mac person. Sure, I've used PCs at work and when I have to but I much prefer the Mac OS. The first indication that there was trouble was when the included setup disk refused to install the printer drivers because they were outdated. There was no link to update, no advice, nothing. So I went to the Brother site and after digging around through their horrible UI, I found the necessary updated drivers, downloaded and installed them. But that was only the start of the hassle.
The user manual is horribly confusing, to say the least, when it comes to setting up the wireless networking (at least to me). I suggest you ignore everything in the manual regarding networking. Let me give you Mac users some hints so you can avoid the wasted time and frustration I experienced:
1. After you've unpacked the printer, installed the toner and paper and printed a test page, go to the Apple web site and search for Brother printer drivers. Apple has all the latest drivers for download free.
2. Download and install the drivers.
3. Insert the CD that came with the printer and open the 'Utilities' folder. Do NOT use the 'Start Here OSX' icon.
4. In the Utilities folder, click on 'Wireless Device Setup Wizard.'
5. In the next window, Setting Up Wireless, click 'NO' then 'Next.'
6. In the next window, click 'checked and confirmed' then 'Next' (you don't need to read the stuff in that box).
7. In the next window, make sure 'Temporarily use USB cable' is selected, then click 'Next.'
8. Connect a USB cable from your computer to the printer.
9. In the next window, you will see the setup software searching for wireless signals in your area. Make sure your network is visible, then select it.
10. In the next window, input your router's wireless access password twice as requested. (Note: if you have an Apple Airport, do not enter the Airport PW, but your wireless access PW. If they are the same, no worries.)
11. Unplug the USB cable to the printer.
12. Click through to 'finish' and you are done!
Your Brother is now set up to print wirelessly and you can put it anywhere you like.