I tried using a regular stylus on the Microsoft Surface, but that doesn't work; the screen is unresponsive. Is there a stylus available or does anyone already have good experiences with another type of stylus?
According to Paul Thurrott's Microsoft Surface: RT vs. Pro, a Specifications Comparison article:
Surface RT : Capacitive pen supported (but not included)
Surface Pro : Includes pen (likely active digitizer-based but not specified)
Pen. A number of readers were worried that Surface RT/Windows RT didn’t support pen input. It does.
Other Relevant Links
Capacitive pen means nothing but finger replacement, i.e. instead of using your finger, the pen tip has enough contact surface that mimics finger touch.
Inductive screen/active digitizer e.g. Wacom are actually screen recognizing pen itself as a special input device.
A few major advantages of having an active digitizer, but in short capacitive can not give true paper & pen feeling, whereas an active digitizer can (potentially).
Accuracy. Try writing very small letters on actual paper with your pen/pencil. You should have no problem. Similarly, a well implemented active digitizer will let you write as small as you can actually write. On the opposite, a capacitive pen needs certain amount of contact surface, therefore you can not write too small. In fact, even regular handwriting size is probably too small for it to be well detected.
Palm rejection. Since inductive technology recognizes the digitizer as a separate input device, if you rest your hand on the screen, it can ignore the palm. Just write things on your paper and you should quickly realize your natural writing behavior is to rest the palm on the paper. Active digitizer can replicate this. However, capacitive cannot distinguish between palm touch and pen touch as it only recognizes that something is touching the screen. So as soon as your palm rests on the screen, you lose writing. Writing without resting palm on the screen for prolonged time is very uncomfortable.
Pressure sensitivity. An active digitizer can send data of pressure sensitivity, i.e. as long as the application supports it, you can actually make a line thicker by writing harder on the screen just as with real paper and pen. There are technologies out there attempting to make capacitive screen/pen pressure sensitive but those pens are very expensive and it's not certain how well they work.
So in the end, Microsoft stating that RT supports capacitive pen seems a bit misleading because any touchscreen essentially supports such as they are nothing but a replacement of your finger. But true underlying technology is not there to replicate pen & paper experience. So if that is something you are looking for, you have to watch out.
Pen input is not available on the Surface tablet running Windows RT.
As Karan pointed out in his answer, there is conflicting information on the Microsoft website and as well, other sources point to there being capacitive pens available for it.
From my experience capacitive pens are generally more like a replacement for your finger, verses a replacement for a pen. But I can't speak to the Surface's specific implementation.
Since you mention you have a Wacom tablet, then here a Bamboo Stylus from them that should "just work".
This is not a product endorsement, there should be plenty others by many other companies to choose from, none of which have I personally tried.
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It will be available on the Surface that runs Windows 8 Pro, which is I believe is slated for release sometime in 2013.
The second link specifically lists:
Pen Input :: Pen input and pen (included with purchase)
This pen (with Surface Pro) will apparently be of the digitizer variety (similar to your mentioned Wacom), which should have the features and resolution more similar to what you're used to with your Wacom.