I don't think there's any cross-browser way of styling it since every browser implements their own calendar differently. The easiest way (if you can use external libraries) is to just use jQuery UI Datepicker, which without styling will just give you a basic calendar popover that you can then customize the styling/positioning with CSS. Let me know if you need help with that.
You can then use the native html5 datepicker/calendar as a fallback for browsers that have javascript disabled
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