Having started with a D50 some years ago, and having been very proud to have it when I did, I will tell you that its low-light performance was nothing to write home about. Yes, you can shoot in S mode and control the shutter speed, thus fighting camera shake from your tremor. If it's dark enough the camera will keep the lens at maximum aperture anyway, but if it's that dark, your pictures will come out dark as well, underexposed.
Raising the ISO can counteract that, but the D50 has a limited ISO range compared to more recent cameras, with a max of 1600. Most modern cameras go to at least 6400, usually 12,800 and even 25,600. I recall not liking the results on my D50 even as low as ISO 800.....
If you aren't getting satisfactory pictures in low light situations, you simply have to add light in the camera (or sensitivity to light) by slowing the shutter speed, opening the aperture (lower f:number,) or raising the ISO (making the camera more sensitive to light.) The fourth option is to use flash.
Reduce the shutter speed: Shooting at 1/125 instead of 1/250 gives you twice as much light, and going to 1/60 gives you twice again. Slower shutter may be more sensitive to shake from the tremor, though. That shake is more apparent at longer focal lengths. It might be fine at 18 to 24 mm on the zoom, but unacceptable at 55mm.
Opening the aperture: f:5.6 lets in twice as much light as f:8, and f:4 lets in twice as much as f:5.6. The maximum aperture of the lens (the lowest f:number) is part of the lens's designation, i.e. the kit lens is an 18-55mm f:3.5-5.6, which means it can shoot at f:3.5 when it's zoomed back to 18mm, but is limited to f:5.6 when it's zoomed to 55mm. If the lens won't open far enough to shoot when all your other criteria (shutter and ISO) are where you need them, then the only lens option is a "faster" lens, meaning one that has a larger aperture. Zoom lenses that are fast are $$$EXPENSIVE$$$ but primes in the 50mm range are not (as far as lens pricing goes.) Downside of a fixed lens, even though it may give you better light gathering ability, is that its field of view may not fit what you need to shoot. 50mm is fairly long on a D50 camera, moderately telephoto.
Raising the ISO: Doubling the ISO number doubles the sensitivity of the sensor in the camera, at the expense of noise. Noise is seen as "grain" in digital pictures, area where color is splotchy instead of smooth and even. Noise is fairly easy to fix on the computer, but the noise reduction that's built into the camera is fairly limited.
If ISO is as high as you can stand it, aperture is wide open, and shutter is as low as you can control it, then you have to add light, either by making the space brighter or by using a flash. Flash creates issues when shooting "shiny" things, especially when shooting shiny things straight on. An image illuminated only by flash also has a surprisingly narrow distance range of correct light level. Anything closer is too bright and anything farther away is very dark. Light behaves with an inverse square rule, so something twice as far only gets 1/4 the light from your flash.
So to work with your tremor, you have to control shutter speed and not let the camera decide that for you. That means S mode, or M mode. In M, you also have to set the aperture, which is tricky on the D50 because you have to hold a button down while turning the wheel. Turning the wheel without that button sets the shutter. So for simplicity, use S mode and let the camera pick your aperture. If the meter display in the viewfinder shows that it's too dark, though, then you have to use a slower shutter or raise the aperture, or use the flash. Lots of things to figure out, but they come with practice.
Shoot some stuff, and take notes of how you shot it. Make a change (just ONE change) and note that change, and take the shot. Compare them. Make another change, and so on. By ONE change I mean change the shutter speed, or change the ISO, but don't change EVERYTHING at once; you'll never figure out what worked then.