How to take photographs like this one?

With the white background like this one? I have Nikon D5100, but no additional lens, flashes, etc. So how can I make a photo similar to this with only my camera and blank white wall?

Well.
This is a good example of the isolation on a white background.
To take a photograph like this, you need a flash with a light defuser.
Better to mount a professional flash on your camera and point it to the ceiling…
Also you need a white plain background like a bed sheet or a really white wall in behind.
Lighting is very important, cool light is preferred and works great.

Then you need some post processing in photoshop.
You can remove the background by curves method or replace color easily.

Give it a try.
Sure you will find your great results.

You just can't take a photo like that without several flashes reflectors etc…

You can try by getting together a few lamps from around your house, point some just at the wall, and some at your model, adjust your white-balance and keep moving stuff around until you get what you want, shoot in manual mode, and adjust the exposure until you are happy.

Simple… You can't.

You can't do it without lighting the wall/background… The model also needs to be lit separately. Classic high-key studio photography requires good off-camera lighting