There are 2 ways to use an esp with Arduino. One is to use the esp as a WiFi module for an Arduino like an Uno. The Arduino sends "AT" commands to the esp over serial lines.
The second way is to use an esp instead of an Arduino.
The esp can be programmed directly with the Arduino IDE. It is a much more powerful and capable processor than an Uno, but an esp-01 is hampered by having so few pins.
It's much easier and better to get an esp development board. I recommend Wemos Mini.