Did it fit in a lab room or was it very small?
What were the dimensions of the gold foil itself?
Thanks!
Here’s a diagram: http://images.google.com/imgres?imgurl=http://www.salem.k12.va.us/staff/sjones/chemweb/atomstru/rutheapp.gif&imgrefurl=http://www.salem.k12.va.us/staff/sjones/chemweb/atomstru/atruther.htm&h=342&w=343&sz=16&hl=en&start=241&tbnid=-xtLKzbgJFSjhM:&tbnh=120&tbnw=120&prev=/images%3Fq%3DRutherford%2527s%2Bgold%2Bfoil%26start%3D234%26gbv%3D2%26ndsp%3D18%26hl%3Den%26sa%3DN
Looks small enough to fit on a desk.
In Rutherford’s article on the subject, he states that the foil was about 0.4 microns thick. No word on what the other dimensions were, though.
The Geiger & Marsden he mentions, by the way, were the one who actually performed the experiment (albeit under Rutherford’s supervision.) Geiger is perhaps better known for being the co-inventor of the eponymous counter.
I can’t find an actual scale diagram of Rutherford’s (and Geiger and Marsden’s) 1910/11 apparatus that led to his hypothesis that the atom had a very small nucleus but there is a diagram of Geiger’s 1908 apparatus here .
As you will see it is a bit under 2 metres long and my understanding is that the scattering experiment was shorter. Bare in mind that practically all physics experiments around this time were sort of “table top” sized. They were generally put together by the researcher him or herself with only a small team to help. Also the funding just wouldn’t allow anything too massive or complex. Another factor encouraging a small size was that the experiment had to be done under vacuum and, when making and pumping down a vacuum vessel, the smaller the easier!
One of my lecturers at Manchester in the '70s had been a student under Bragg who in turn had worked with Rutherford and he was forever going on about the good old days when all experiments were done with scrap metal, sealing wax, and string 
We reproduced the experiment during senior lab in college, and the apparatus easily fit on a lab bench. Rutherford’s great-grand-nephew took me to Homecoming one year in high school and showed me some family photos of Lord Rutherford’s lab. I believe that the featured apparatus in one series of photos was the gold foil apparatus and it was a little more, you know, steampunked, than the ones from college…but not much bigger.
As MarcusF’s link makes clear, there wasn’t really the Geiger-Marsden experiment - it was a series of increasingly refined experiments that they did over a period of years. With Rutherford’s 1911 paper providing the theoretical legwork to support his interpretation of their results.
The diagram beowulff linked to comes from one of the later papers in the sequence, specifically this one by them from 1913 in which it’s Figure 1. The paper’s text explains that the distance R-S, between the source and the screen, was about 4.1 cm, so the whole diagram shows a piece of apparatus about 10 cm across.
Similarly, the version of the apparatus that’s in Figure 3 of the same paper has a cylinder that’s about 8 cm in diameter and perhaps 20 cm in height.
So the actual apparatus was indeed pretty small. However, it’s clear from the stories told about doing this style of experiment at the Cavendish in the Twenties by their contemporaries that much of the difficulty in doing them well was getting sufficient darkness to absolutely maintain night vision and hence sensitivity on the part of the observers. Furthermore, nobody could reliably maintain the necessary concentration for very long - though Chadwick was the whizz at it - so they were having to work as teams of several people in the dark. The surroundings in which they were working and recording the flashes was thus rather crucial and the whole lab became a very controlled environment. They were building special booths in blacked-out rooms and using special buttons and electrical counters to keep track of what had been seen.
In other words, in practice the experiment was taking up rather more space than a small patch of desktop.