Yahoo mail is second largest email service where you can make a yahoo account for free. You can also use this service without having difficulty, so you can follow here few steps to sign up yahoo mail.
Input complete details(first and last name, email address, password, mobile number, date of birth and your Gender)
Now, click on continue button
Next window, you click on text me an account key to verify the mobile number
You receive a text message or code to your mobile number. Enter code and click on verify button to complete process of yahoo mail account creation.
Also read this - How Do I Make a Yahoo Email Account Without a Phone Number?