Neither the owner's manual, nor Sony's website offers any Mac OS specific instructions for connecting their Sony BDP-S570 Blu-ray / DVD Player to your wireless network. Internet searches and product review have some help. The Auto wireless method doesn't work, you have to set it up manually.
Here are the steps I followed (there may be an easier way to do it).
1. Connect your player to your network using a wired connection. Though your goal is to eventually connect your blu-ray player wirelessly to your network, the hardwire connection simplifies the firmware update. So, run an ethernet cable from your player to your wireless router. Then on your Sony player go to Setup: Network Settings: Internet settings: Wired Setup: Auto: Save & Connect. It connected to the internet fine for me this way.
2. Perform the latest firmware update following Sony's instructions, "Blu-ray Disc™ Player Firmware Update (version M04.R.491)" posted on their support site. The update version may have changed. The instructions says nothing specific about a Mac, just follow the network update method at
http://esupport.sony.com/US/perl/swu-download.pl?upd_id=5686&mdl=BDPS570
I wanted to do this step first in case the update effected something that would effect the wireless setup process.
3. Write down the MAC address of your Sony player's wireless ethernet under Setup: Network Settings: Internet Settings: View Network Status; scroll down to find it.
4. Set up your Sony blu-ray player's IP address manually on your Time Capsule/Airport: Launch Airport Utility on your Mac: Manual Settings: Select the Internet icon from the toolbar: Select the DHCP tab: Select the + sign under DHCP Reservations: DHCP Reservation Setup Assistant; enter a Description of your player like; "Sony BDP-S570 Blu-ray Disc / DVD Player" or whatever; Select MAC Address under Reserve address by; click on Continue: enter in you Sony player's MAC Address that you wrote down earlier (it has to be exactly right, don't confuse O for 0's. Next choose a reserve IPv4 Address for your player. I set mine as 10.0.1.20; click done: Click Update to update your Time Capsule with the new settings.
5. Once your network restarts, from your Sony player go to Setup: Network Settings: Internet Settings: and select Wireless Setup. Then Manual registration: Manual registration (again): enter your SSID (the name of your network): Choose your network security protocol; I'm using wimpy WEP, I forget why. Enter in your passphrase. Select Custom for IP address and proxy server settings...: IP Address Setting: Manual: IP Address use the one you entered using your Airport Utility; here are my settings: IP Address 10.0.1.20; Subnet Mask 255.255.255.0; Default Gateway 10.0.1.1; Primary DNS 10.0.1.1; Secondary DNS 0.0.0.0: Do you want to use a proxy server? No (I don't have one). Select Save & Connect.
Your player should now indicate that it has connect wirelessly to your network and your internet.
Good luck!