You can't just slather grout over any porous or uneven surfaces such as split-slate tiles or limestone or similar stone tile that has crevices, holes or open cracks. The grout will fill in those areas and even if you're able to clean them out, you'll never have enough time to clean everything before the grout sets up.
Here's an effective three-step system. It takes longer than conventional grouting techniques, but you'll get perfectly clean tile with far less hassle.
The only special tool you might not have is a grout bag, which masons use for tuckpointing. Find one with the masonry tools at the home center. Also pick up a bottle of “grout release” at a tile store. To start, clean out all the grout lines by vacuuming and scraping out any thinset projecting above the tile. Then wipe the surface with a damp rag until it's free of dust.
The three photos show how to apply the grout. When you're finished with one batch, let the grout set until you can't leave a thumbprint in it. Then begin tooling the joints with a slightly damp sponge to shape and even them out. Keep wiping away any excess grout until the tile looks clean.
After you see a hazy film form, polish the tile with a dry cloth just as you would with conventional tile.