Serial read in ESP8266-01 not working
A circuit diagram or photo would help, but I would guess you have taken the lead from the PC that is marked Rx and connected to the pin on the ESP marked Rx.  That's the wrong thing to do.  Firstly the PC will use 5V and the ESP uses 3.3V, so you need a little board called a level shifter something like this 2 channel level shifter.  This will let a 3.3v device talk to a 5V device.  Some ESP boards are 5V tolerant, but I don't know what you have so ...

Then when you "talk" over serial you need to cross the Tx and Rx between the two devices, so the can 'hear' each other

 PC - Tx  ---&gt; Rx - ESP
 PC - Rx &lt;---- Tx - ESP


(Lots of other level shifters are available and a lot are cheaper than the example shown, a lot cheaper!)