Good afternoon! 
I have a small issue, because I don't know how can I save data(some int numbers in my case) after turning Arduino off. As long as I am turning on my Arduino all data resets.
Do I need to write something in my code or to buy some components for solution?
Please answer me, I have no idea. 
What type of arduino?
Many types have EEPROM memory.
I use Arduino Nano 3.0 Atmega328
Does it have EEPROM?
Great. That has 1K EEPROM. Check out the examples in @oldcurmudgeon 's link.
What are the values you want to save in your project? What is their purpose and when do they change?
Of course, you can't save data after the Arduino turns off. But you could do it just before it turns off.
Better still is to save the values when they change, then it doesn't matter when the Arduino turns off.
I was only thinking about project with time manager. As Arduino has EEPROM I'll check that library.
Thank you very much! 
You can use a SD-card board.