Here is what I did to get my TEW-637AP to work at 300Mbps:
1. Set up using the CD-ROM provided. It is important to only use WPA2-PSK using the AES algorithm or disable wireless security.
2. In the AP's web interface set the following in Basic Wireless Settings:
Repeater Mode Support: Disable
Wireless Mode: 802.11n only
Frequency (Channel): Select a channel from 1 to 11 that is free (12-13 does not seem to work). You can use inSSIDer to find a free channel.
Operating Mode: Green Field
Channel Bandwidth: 20/40
Guard Interval: Auto
MCS: Auto
Reverse Direction Grant: Enable
Extension Channel: (set automatically)
At this point I got 300Mbps reported in the wireless connection dialog box. However the actual throughput will never be this high. You can use the program LAN Speed Test to do some measurements of actual throughput. I got around 70Mbps as I was using 100Mbps switch.
More interesting info can be found here:
http://www.smallnetbuilder.com/wireless/wireless-basics/30664-5-ways-to-fix-slow-80211n-speed