I just bought an Esp8266(not the node MCU) and tried connecting it with Arduino without a USB to serial converter but in vain. I am a beginner and don't know what to do. It is not responding to AT commands. Can anyone give me a detailed step by step process to connect it?

I am using Arduino UNO R3.

This is my connection diagram:-

I uploaded an empty code(Bare minimum example code), just to see if the AT commands are working, but it failed to respond. I reflashed it, then also it is not working. when I type AT it shows nothing. But if I shake it, sometimes it shows gibberish.