Tile is a relatively durable surface that is easy to clean. However, the porous nature of the grout between the tiles leaves it more vulnerable to stains, such as those from oranges. Your best bet is to avoid having your grout get stained in the first place by sealing it. You can purchase commercial sealers that can be applied either with a brush or with a spray can. The sealers go on and dry clear and quickly and will help make the grout water and stain resistant.
If your grout does get orange stains on it, you can try to remove them by dipping a toothbrush in soapy water and scrubbing lightly. If after a few minutes the stain has not completely lifted, dip the toothbrush in hydrogen peroxide and continue scrubbing. The hydrogen peroxide should lift the color from the grout without damaging the grout.
If the orange stains are stubborn and are not removed with soap and water or hydrogen peroxide, you can try to use bleach. The use of bleach is not recommended for grout because over time it can cause the grout to break down and become damaged. But, use on a single stain will likely not cause much damage. Dip a toothbrush in a half-and-half mixture of bleach and water and scrub the orange stain on the grout. If the stain persists, dip a paper towel in the solution and lay it on the grout and let it sit for several hours. Be careful when using bleach because it will lift the color from colored grout as well as color from your clothing.