I am afraid you've bitten off a bit more than you can chew at the moment, but don't despair.
You are missing a whole lot more than a few basics and I can say that because I've made this work and had to learn a few things the hard(ware) way.
My current state of knowledge about the Arduino WiFi shield, or better the current set of libraries do not yet support the UDP protocol and there have been a numer of posts about this unfortuante fact on the forum. But that may be different now. That is important because the OSC protocol generally is based on UDP and ArdOSC is no exception.
If the Arduino WiFi shield does support UDP, you have another few hurdles to take. ArdOSC makes use of some lower level functions of the original Ethernet shield library that talk directly to the W5100 Ethernet chip on the Ethenet Shield through SPI. You'd have to rewrite these functions for the specific hardware of the Arduino Wifi Shield.
The above are most of the hardware limitations. There is one more that has to do with the memory requirements of the involved software libraries so an Arduino version with more memory, e.g. a Mega would work if you need space for your own code.
However, you can deal with all of the above if you are not shy of getting different hardware. E.g. Get an Ethernet shield, so you can work with ArdOSC right out of the box. If you want WiFi, then connect a little pocket router to it. I've used a TP-Link TL WR703n and a 702n. I'd recommend the 702n as it has a English user interface (if you buy it through regular US sales channels) the interface for the 703n is all Chinese. You can get the Ethenet shield on eBay for about $20. As long as it has a W5100 chip on it you should be OK. The router will set you back about $25. Together, IMHO that provides you with a lot more mature functionality than any of the WiFi shield currntly available at a much petter price point.
The next thing you are missing is that the reason services show up in TouchOSC is because these are services that are announced through Bonjour Bonjour (software) - Wikipedia
For TouchOSC to pick the Arduino up, you need to use the Arduino Bonjour library to register a service on the WiFi network that your iDevice is connected to.
BTW, the Bonjour Library also makes use of some lower level functions of the Ethernet shield library!
In my LED lighting systems instead of an Arduino I use the Arduino compatible Teensy++2 http://www.pjrc.com/teensy/with a WIZ812MJ Ethenet module http://www.saelig.com/BRD/ETH042.htm and adapter also from PJRC. Together, including the router, all that is less expensive than the Arduino WiFi shield alone!
So, if I have not severely scared the crap out of you and you still want to go ahead with your project and are not afraid of occasionally pulling out your hair and are ready for a few setbacks, in that case you are in the right ace here and I'd be glad to help you along. Once it starts working its actually pretty darned cool!!!
Perhaps start with what you actually want to achieve as an end result and we'll go from there.
I have created a sketch that works perfectly if I connect directly the ethernet shield to my computer. I have bought a TL-WR703N and flushed a modified english firmware to be able to use it properly. I set it up as a client and connected it to my computer and configured it to connect to my Home Router to be able to access the internet. I disabled my laptop's wifi card and only by using the WR703N as a client I was able to access the internet. Then I assigned a static IP address to the WR703N from my main Home Router and port forwared TCP-UDP ports from 80-5881 for the specific static IP. Then I plugged the WR703N to arduino and tried to reach the server locally but I couldn't. The WR703N was pingable at the local IP but I just couldn't reach the arduinos server. What did I miss?