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Follow the mixing instructions that came with the grout. Don't use more water than the manufacturer recommends or the grout may not work properly. A grout float is a thick rubber pad with a handle on it that's available at most home improvement stores. Scoop some of the grout mixture out of the bucket using the padded part of the grout float. Press the mixture down into the gap you're repairing until it's completely filled. Don't worry if grout gets on the surrounding tiles. You'll be able to clean it off later. Hold the float so it's at a 45-degree angle with the floor. Slowly drag the edge of the float over the gap you filled to scrape up the excess grout and make the grout flush with the rest of the floor. After 20-30 minutes, the grout should feel firm to the touch. Refer to the instructions that came with the grout for specific drying instructions. Wet the sponge and squeeze out all the excess water before you use it. Don't use a soaking wet sponge or you could damage the new grout. Press down lightly as you wipe the sponge over the new grout and any nearby tiles that got grout on them.
Mix the grout powder with water in a large bucket. Use a grout float to fill the gap with the grout mixture. Wipe away the excess grout with the edge of the grout float. Let the grout dry for around 20-30 minutes. Clean off the surrounding tiles with a damp sponge.