Arduino is a combination of hardware and software platforms. The Hardware that we are using is the Arduino Nano and the software used for writing programs is the free Arduino Integrated Development Environment (IDE)
The Arduino IDE will run on most PCs and can be downloaded and installed from https://www.arduino.cc/en/Main/Software. We recommend the use of the version that is downloaded and installed on your computer rather than the web editor, as this can be used without having to have a continuous internet connection. Follow the instructions for your type of PC from those on the links at https://www.arduino.cc/en/Guide/HomePage
As well as the IDE software for writing your programs, you will need to install a driver on your PC which allows the PC to send programs down a USB cable to the Arduino Nano. Which driver you need to install depends on where you buy your Arduino Nano from. If it is a full price Arduino one, the standard installation will include a driver for it. If it is a cheap one from EBay it is likely to need the CH340 version of driver which does not come with the standard Arduino installation. You can download and install the CH340 driver from this web site https://sparks.gogo.co.nz/ch340.html
There are lots of online resources to help you to learn how to write Sketch programs for the Arduino Nano. The best place to start is with the Arduino web site tutorial pages at https://www.arduino.cc/en/Tutorial/Foundations
Once you have loaded the IDE and opened the Arduino program you will see the window as shown below. You will find lots of examples to help you if you click on File / Examples.