The serum is the first skin care product that you will apply after having cleansed the skin. Serum has a light, watery texture and can be easily absorbed by the skin. It should be applied before your moisturisers or other skin care products, since their texture is thicker. If you apply it after your moisturiser, the serum won't be properly absorbed by your skin and you won't benefit 100% of the effect of your serum.
Depending on the skin issue you have you want to choose your serum. If you have acne problems then you want to choose a serum that will help you treat to heal or treat your acne. If you have dry skin, you want to choose a serum that is hydrating. I guess you have understood the principe yet.