When talking about names, we tend to use the number of strokes. For example if your surname is 王 (Wang), it's 4 strokes, and will be placed before someone with the surname 张 (Zhang), which is 7 strokes.
Another order is for dictionaries. Sorted by PinYin, so it's from A to Z. Also in the back of the dictionary there is an index based on character parts. For example, 杉 (Shan1, means fir, a type of tree) and 枝 (Zhi1, means branch of the tree) will be under the 木 (Mu4, means wood) part. You can find the character by part, then it will tell you which page this character is on.