It looks like it's been over four years since this was addressed here. Old answers to this settled on a single input for the entire date (with a hint for formatting).
But I see that Google uses a drop-down for the month in their sign-up form:
And the US goverment web design standards site uses three input fields: https://playbook.cio.gov/designstandards/form-controls/#date-input
Additionally, what do you think about the label? Birthday vs. Date of Birth vs. Birth Date
As a user I prefer seeing a drop down for month selection (the way Google does it) . Especially because it happens frequently that I fill forms on my mobile.
And I also like it when the software is smart and knows how to convert my input if wrong. For instance if I wrote "82" in the year box it should just know it's 1982.
It's not recommended to display a calendar for Date of Birth, which is the context of this post, not, for example, booking a hotel room by date. Calendar's default values display today's date, so navigating back in a calendar to say, 1972, would be a painfully long experience.
Good design will provide both keyboard and mouse input access. This means the 'Date of Birth' component is a combination of a single text edit field (with hint text - mm/dd/yyyy) and a calendar interface. When the user tabs in the field display the calendar (without blocking the text input). Provide user the option to either use his keyboard to enter the date directly or mouse to interact with the calendar. If the user uses the keyboard, add the forward-slash automatically.
Recognize the device, if it's mobile device, disable text edit field and allow input via calendar interface only to reduce manual errors.
Everybody understands 'Date of Birth' label. 'Birthday' sounds casual, unless you are working on a non-professional application.
Using a dropdown for the month name is ideal when you have a wide-range of users all over the world. They don't have to think about whether MM or DD comes first or second. Everyone's familiar with month names.
If you're just using numbers though, three separate fields are best to get the most accurate data. This article "Bad Practices on Birthdate Form Fields" explains that if you don't use a menu users don't have to switch their hands from mouse to keyboard, it can just remain on the keyboard. The length of the text fields works as cues for indicating format input. And writing out the labels instead of abbreviating them prevents users from mixing up MM and DD if they have a habit of typing their birthdate in a certain order.
