The folks at OS X Daily apply a common PC solution to the iPhone:
If your wifi internet seem slow on your iPad or iPhone you can modify your DNS to speed things up. (This isn’t always the issue, but it can make a difference.)
1. Find a better DNS. Usehttp://code.google.com/p/namebench/to locate one on your computer – if your computer is on the wifi network you want to speed up. If you don’t have a computer, don’t want to download the program or are to lazy you can use google’s DNS which is fast but not always the fastest. Google offers either 18.104.22.168 and 22.214.171.124
On your iOS device:
2. Open Settings
3. Go to “Wi-Fi” and tap the blue arrow next to your network of chic.
4. Touch the numbers next to “DNS” and replace them to your above DNS.
5. Using the button “Wi-Fi Networks” back out to save the setting.
Tip: OS X Daily