Here are a bunch of great tutorials https://www.hometalk.com/search/posts?filter=clean%20grout
I use vinegar, warm water and a toothbrush. Labor intensive, but works like a charm.
18 months ago I used the HomeRight Steam Cleaner to clean the white grout on our marble on our master bathroom floors. It did an amazing job. No chemicals, no cleaners. It still looks great, although probably due for another clean.