To open an account online, you can sign up using your mobile number by clicking on the link down below.
https://zerodha.com/open-account?c=ZMPVZO
You will receive an OTP to your number and you can get started with the process.
You will be required to enter your PAN, bank account details and personal details to continue with the sign-up. Check out this video.
NOTE: This video is uploaded in July 2020, Now there is a slight difference in the steps to be followed, but overall the process is the same. Please refer to this video and do it accordingly.
If you face any difficulties while opening an account online, you can contact us on this number 9995969780
Alternatively, you can create a ticket by clicking on this link https://support.zerodha.com and they will contact you or you may contact Zerodha directly at — +91 80 4718 1888 / 080 47192020 / 080 71175337
You can do this anytime, It will never affect your trading if you dint courier it