Hi Lea. Here is a link to some great posts on cleaning grout... https://www.hometalk.com/search/posts?filter=clean%20grout
I keep mine clean by mopping liberally with this solution:
1 cup baking soda
1 cup white cleaning vinegar
1 Tbsp blue Dawn
2 gallons hot water (boil 1/2)
If grout is stained clean with Lysol Toilet bowl cleaner in the black squirt bottle and Mr Clean Magic Eraser.
Check to make sure your grout is sealed. If not, then once it is clean seal it to make maintenance easier in the future.