Understand the basic nature of an Arduino; find the Arduino software tools.
The Arduino is a tiny computer with specialized hardware suitable for physical interfacing and easy programming. Or rather, there are many variants available in different configurations which share a common programming system and design philosophy. We'll focus on the basic Arduino Uno.
The Arduino runs programs from built-in FLASH read-only memory. When powered up, it boots very quickly and starts running the stored program. This is convenient for physical interfacing; the world doesn't wait for booting up. It is low-power and works reasonably well with battery supplies. It has built-in analog-to-digital conversion for reading analog sensor inputs. It can generate pulse-width-modulated (PWM) signals for operating servos and motors. It doesn't have any sort of graphic display, so understanding and debugging program flow requires a host computer and careful reasoning from the limited data that can be sent to it.
The Arduino comes with a software application called the Arduino IDE (or Integrated Development Environment) which combines a program text editor, a compiler which translates the program text into machine code, and a bootstrap loader which can program the machine code representing your program into read-only memory on the Arduino microprocessor.
The identity of the Arduino is rooted in the programming language as defined by the supplied libraries. The underlying language is C++, but the built-in libraries use a selected subset of C++ to keep the syntax beginner-friendly.
The computational capacity of an Arduino is vastly smaller than a contemporary laptop or cellphone: the Arduino Uno has only 32K of ROM and 2K of RAM, executing 8-bit instructions at 16 MHz. The laptop computer used to write this text has 8 million times more persistent storage and 4 million times more transient storage. Computation rates are harder to compare, but the basic clock rate of this laptop is 80 times faster, and the effective processing rate even more multiplied. But the Arduino consumes substantially less power, and is substantially easier to program at a hardware level.
The IDE package actually contains all of the source code for the libraries, so with a little digging it is possible to read everything that is compiled and loaded.
The Arduino Uno circuit diagram can help with understanding all the parts on the board. There are actually two microcontrollers, with one devoted to the USB connection, and the other running user programs and interfacing to the pins. The 3.3V supply is provided by a linear regulator attached to the 5V supply. The power supply automatically switches between USB and external power. The USB supply is fused to try to protect the attached computer from short circuits.