Step one: Mix 1 c of baking soda with 1/3 c of water and place it into the cracks. I just ran it along the grout, no need to pack it or anything.
Step 2: Place 1 part water 1 part vinegar (1 c/1 c of each) into a spray bottle. I sprayed down the baking soda/water filled cracks. It bubbles a little.
Step 3: I then took a bristle brush and gave it a quick scrub and then wiped it clean.
Here's a picture with one row down and the rest of them...well, not....I guess I better get to work on that. It's hard to tell the difference in these night time/winter pictures, but....trust me, it's pretty amazing. The one row was b/c I totally didn't trust it, but...I really did finish the grout and it looks great. Plus....baking soda, vinegar, and water are more in my price range!