Why do my pictures turn out shaky - Nikon D3100?

So whenever i take portrait pictures of any of my friends, it turns out pretty shaky even though i have an alright hand, it doesn't shake that much. I use Auto mode, tried Manual as well, but whenever i change my Shutter speed to 1/250, it turns out pretty dark since i took the pictures in a dark area, which means i wouldn't get it as dark if it was sunny. ANYWAYS, do you know how i could fix the shakiness, Thank you FOR YOUR TIME.

As you breathe, your body moves, including your hand. Your shutter speed is so slow that the camera picks up on the minute movements of your hand. Use a tripod for that speed and slower with a cable release. The idea is to stabilize the camera without touching it at all. Using a tripod without a cable release defeats the purpose of the tripod.

Well, the biggest problem is that you clearly do not know how to use a DSLR camera…

To limit camera shake, you need to increase shutter speed or use the flash. If the photo turns out dark when you increase the shutter speed, open the lens aperture more or increase ISO to compensate.

You should be embarrassed that you have a DSLR but do not even know the very basics of exposure. But hey, at least you LOOK like you know what you're doing while holding that big black camera right? Shameful.

1/30th to 1/60th of a second is the limit for most people on holding a camera still using a normal/kit zoom lens. As you go to a higher power zoom, the rule of thumb is 1/100th for every 100 mm. So if you are using a 200mm telephoto, then your shutter speed should be at least 1/200th of a second to eliminate camera shake.

When you get to the slower speeds, you can either use a tripod to eliminate camera shake, a flash (which allows you to remain at 1/60th of a second), or turn on the lens VR if it has it. VR will help, but not eliminate camera shake if you go below 1/15th of a second (unless you don't hold the camera very well).

Finally, you can also increase the ISO, but this has side effects of introducing noise in the photo if you set it too high.