Slingbox will certainly do what you're asking for, and it does a remarkably good job of it. Once you get past the initial setup it's a load of fun to use.
The quick answer to your question is that setup needs to be run from a computer at your sister's house the first time. After that you can do it yourself from Ireland if you want to make any changes. Note that this same-network stuff only applies to initial setup (or after a hard reset). Once you get it up and running, you can watch Slingbox and make any minor configuration changes from anywhere on the internet.
It sounds like you have found the relevant support documentation on how to get a new Slingbox working, so I'm not going to "reinvent the wheel" and write out step-by-step instructions. It would probably just confuse things. Instead, I'll write down a some overview comments and a few tips.
If you're still unsure of what to do after you read this, post back and say so. I don't mind going into further detail if it will help.
There are two general steps to get things working:
- Setting up the Slingbox
- Setting up Remote Viewing
Setting up the Slingbox
This is done with the Setup Assistant, which is a part of the SlingPlayer viewing program. If you're using a WIndows computer and have a current-generation Slingbox, it can also be done from a website. Mac users should stick with the dedicated full SlingPlayer program.
Setup Assistant is where you tell the Slingbox what video sources you've attached to it, and how it should talk to your router so it can send a TV stream to computers you would like to watch from.
The first time you do this with a Slingbox or after a hard reset, Setup Assistant must be run from a computer that is connected to the same home network that the Slingbox is connected to.
This is necessary because in both cases the Slingbox isn't ready to communicate with computers outside the home network until you have enabled it to do so in cooperation with the router. Think of it like this: it can't go outside the house until you tell it where the front door is. Once it's set up the first time, you can re-run Setup Assistant to make changes from anywhere.
Since you're far away from the Slingbox, the clear and easy option is to ask your sister to run initial setup for you from her computer. Get her on the phone and point her in the right direction- It's pretty easy. If she was able to do the physical install and hook the wires up, using Setup Assistant ought to be a breeze.
A popular but more complicated option would be for you to take remote control of her computer. From Ireland, you would see her screen on your computer and have keyboard/mouse control of it as if you were sitting in her house. Then you could run Setup Assistant yourself as if you were there.
I went this route with my dear Mother. She's wicked smart and very handy, but all the clocks in her house are blinking midnight. Techie stuff drives her nuts and she would prefer her computer to work like a toaster. I coached her though installing Logmein.com over the phone so I could take control of her Mac as needed- works like magic. Now I can help her when she has computer questions just like I was sitting next to her. If I was only interested in initial Slingbox setup though, I would have just had her run Setup Assistant for me and left it at that.
Logmein.com, Windows RDC, VNC are examples of decent, free remote control systems. If you don't already know what RDC or VNC is, definitely go with Logmein.com.
Setting up Remote Viewing
This is part of the Setup Assistant. Early in the process it'll ask you if you want to set up remote viewing. You need to answer yes.
Remote Viewing = watching/configuring Slingbox from outside the home network, over the internet. This stuff doesn't apply to computers inside the house.
Routers typically block this from working as part of their security features. Specifically, a router's firewall prevents things on the internet from talking to things in your house without permission.
Setup Assistant can usually figure out how to make this work on it's own. If it has any problems, you can manually fix it by going into the Router's configuration and telling it to allow Slingbox traffic through on Port 5001.
Hope this helps !