Being a flash based game of course Settlers will not play naturally using the standard Ipad browser and not even with some of the so-called Flash ready ones (Skyfire, Photon, 360). There is however a few solutions that work really well.. Cloud Flash apps.
Several Apps out there provide this form of remote flash where you use a browser to connect to a remote machine that actually runs the flash and transmits it back to your ipad. These suffer from delays (that range from slight to terrible often dependant on how busy the service is) and limitations of service.
Three useful Cloud Browser apps are:
ISwifter

The original cloud browser that works pretty well. You can navigate and build with a fair amount of ease but like all the browsers it has a problem with moving around the field of play and you instead need to use the number pad to jump around sectors.
It can be slow to update the screen and clunky in your ability to place buildings with any accuracy due toa poor mouse interface.The free version requires you navigate to and login into the game each time but it does have a bookmark system to get to the game quickly.
There is a free trial period that you can use to check it out as an option but it is far from the best solution in the long term.
CloudBrowse

This one is an odditty as it has been rejected from the Appstore after previously being available and now can only be found via Cydia and other appstore replacement services... The game plays really well on the service and is a real option for longterm play.
The zoom mouse function is handy for accurate placement of buildings but is not quiet as good as the mouse system in pandaview. Delays are minimal and dont tend to take away from the experience. All in all it is a decent system that can be used to play the game with a good degree of enjoyment.
The free version requires you navigate to and login into the game each time as it does not store any history.
The App does require payment for use but joyfully it is free to download and try in 10 minute windows of free use before requiring a relaunch; so you can either pay or try n play in snatches, which gets pretty tiresome.
Puffin Browser

This one is the best by far for interface, ability to scroll and interact with the game. The controls are responsive and the delays very minimal.
The dedicated mouse and keyboard are simply perfect for play and allow highly accurate placement and interaction. Even better is the scrolling around the land with a mouse that is the easiest system by far. A big plus is that it remembers your browsing history and login information making connection to the game swift and easy.
It does suffer from some random display glitches that paralyse small sections of the screen but a simple tilt corrects them and they are a very minor inconvenience.
If you are going to play TSO on an Ipad this app is the one to purchase.