Instead of connection RX of board to TX of convertor (and vice versa) you have to connect RX to RX and TX to TX.
When you're new, don't start with a separate ESP (ESP-01 to ESP-14) module.
Get yourself a proper development board: NodeMCU - WeMos D1 - WeMos (UNO form factor) - Witty Board
ESP power requirements are 3.3V±10%@350mA
The ESP8266 IS NOT 5V tolerant on ANY pin (see item 5.14 on page 25 of the FAQ)