First of all, visit the URL here(developer.salesforce.com)
You can see the Login Button; click on it.
Fill out the form to signup for a developer Org.
After completing the form, click on the Sign me Up Button, and you will be redirected to a screen like this.
Visit your Email Account. You will receive an email with your username click on the given link to set your password.
Set Password along with security Questions for your Salesforce Org and proceed further.
Now you will be redirected to your Salesforce Org.
NOTE Make sure your Username should be in the form of an Email Address, for example, salesforcesky@dev.com