The broadband box "should" be plugged into your main phone socket, that is the primary point from which other extensions might run.
You can try plugging it into an extension but you might not get the speed that you should, it depends on how good that extension is. I've worked off extensions before without problems, but they can be tricky.
"If I get another one, do I just plug it into a phone socket or do I need a filter thing."
Do you mean that you're thinking of getting a 2nd broadband box and plugging it in as well as your current one thinking that that will extend the wireless coverage.
If so that's not the way to go.
You can only plug one broadband box onto your phone line at any point in time. That box is the link between you and the internet and you only want one of those.
The first thing to do is to try and site your broadband box better. Having it buried away behind cabinets isn't a good thing, trying to have it fairly open can help. If you've got two aerials on it then I know some people who swear by standing one straight up and the other at 90 degrees to it.
In an ideal would you'd try and run a cable from the main box to your computer. Cables are pretty cheap, but fitting them can be tricky and/or unsightly.
One option would be a wireless repeater. You'd place this roughly halfway between your current box and where you want your machine to be. In effect it listens to the WIFI from the main box and then shouts it out again so that it can be "heard" from further afield.
You can get information on those here:
www.broadbandbuyer.co.uk/Shop/ShopSearch.asp?CategoryID=259
A final option might be "ethernet over powerline" or what is known as HomePlug. In short that turns your home power cables into network cables. You plug a gadget into a powersocket near your broadband box, another one next to your PC and then connect that gadget to your PC.
You could even conncect that second gadget to another wireless router and have an entirely new wireless network upstairs.
There's more information here:
www.broadbandbuyer.co.uk/default_ShopGroup.asp?ShopGroupID=61
There are many ways to deal with this so don't worry about coming back to ask more questions.