However I don't think this post is about minimalist web-design as such. I say so because if you want to learn to do minimalist web design this isn't a useful guide (I am aware it's not mean to be a tutorial but it does offer some observations that can lead you the wrong way)
The number one thing you need to understand as a designer if you want to do minimalist design is typography and to do so properly takes years. It's a very refined art to do well and most people get it wrong when they try.
Putting few things on a screen is not minimalism and the Google screen is in itself not an example of minimalism. It was never really a conscious effort but rather a "lets remove everything and just add the search bar and a logo".
What google screen however is a good example of is first principles. I.e. going from the categories based search engines of it's time to a purely search focused approach and using pageranking rather than humans to determine results.
If you want to understand and do minimalist design learn typography first. Besides practicing a lot, a great book to do so with(a classic) is "Elements of Typographic Style" by Robert Bringhurst. It wont teach you typography on the web but it will teach you about typography which is one of the keys to understanding minimalism on the web. Would also recommend Grid Systems by Josef Muller Brockman which also provide a good foundation for understanding typography.
What google screen however is a good example of is first principles. I.e. going from the categories based search engines of it's time to a purely search focused approach and using pageranking rather than humans to determine results.
Just my five cents.