Firstly, hi!
I USED to be a member here under another name (which I have long forgotten) so this isn't my first ever post. It is however my first post in a long while.

I have a laptop which is part of a domain at work, but mostly lives at home. I would like to set up basic file and printer sharing. I have looked into this myself for the last hour or so. Earlier I was about to simply change "domain" to "workgroup" in the computer name bit. However, as my finger hovered, poised over the mouse button I was suddenly overcome with an ominous feeling of dread, and sensed the lurking presence of an almost unspeakable evil.  Actually, I made the last bit up. I'm guessing it really isn't a GOOD idea though...

We have 2 computers. ONE is the aforementioned laptop, the other one isn't (upstairs, home desktop). Both connect wirelessly to the internet thru Sky's own netgear router. The printer I would like to be able to share is connected to the home PC.

At the MOMENT there isn't any sort of network infrastructure in place. The upstairs comp may, or may not, be littered with the remnants of previous disastrous attempts at networking (I can't really remember)

I have gone on too long; in the event that this thread recieves any replies I will be happy to provide additional info.

Thanks in advance

Well since your post made me chuckle a few times with your funny remarks I will reply to it. 

In your laptop at the login screen you have 3 fields. They are username, password and domain. At work you normally would type your assigned user, pass & your company's domain name. You probably do that at home too. However, I would suggest that you keep you login to your local pc when at home. So at the login screen you would select for domain "YourPCname (this computer)" option. For the login name you may need to get one created since the one you use for the domain may not exist as a local user. Then you can assign the local user account to the workgroup that your home pc is in without affecting the domain part. After that it is just a matter of sharing out your printer.The best bet for you would be to contact your IT person at work and discuss this with them. Since you are using a laptop provided by your employer there may be restrictions in place KEEPING you from being able to do what you want.

I also have a company provided laptop that I also use at home. Due to company policy concerning security of company information that may be on my laptop I had to get permission to be able to use my computer online while at home.

So before you start following advise on how to be able to network this machine at home it would be good to check with you company IT department. Additionally they should be able to give you all the assistance you need.