To easily create a favicon.ico to be used on a website, you can use the following website. Here you can either enter the URL of the image or upload the png logo you want to use; then a download link is created where you can download the ico:
Some tips for you favicon image.
The normal size is of 16×16 pixels. For Apple devices like the iPhone and iPad, one can provide a custom icon that users can display on their Home screens using the Web Clip feature whose recommended size is 57 x 57 pixels, with 90 degree corners.
However with the more recent higher definition screens on Apple’s products, Apple has their icon at 129 x 129 pixels.