Send AT commands to ESP8266 from Arduino Nano serial monitor
First problem is that io 0 of the esp8266 must be pulled HIGH for normal boot. With io 0 not HIGH, the esp8266 starts in flashing mode.

Your other problem is the reset pin connection. It must be connected with pull-up resistor or not connected.

See ESP8266 Hardware Design Guidelines


  Pin32 serves as an RST pin which can be left floating when it is not
  used. The reset pin is held low when the chip is enabled. In order to
  avoid resets caused by external interference, the lead is generally
  required to be short, and no external pull-up resistor is necessary


I suspect that "The reset pin is held low when the chip is enabled." is a bad translation. They say in pin description "32 EXT_RSTB I External reset signal (Low voltage level: Active)". What they mean is that the chip resets when reset pin is set LOW.