It depends on how big is your spilled area, if it is small section, you can use paper towel simply wipe things off. If it is a big spilled area, you can use your garden hose to spray clean the artificial grass lawn, but if there are any solids from your spills, you will need to pick them up before spraying or spray them to the side and pick them up.
If you need a good thorough cleaning for the entire area of your artificial lawn, you can use normal detergent to attach to your garden hose and spray clean it. Normal detergent will not damage your artificial grass.