How do you know when a burn requires medical attention?

Depends on severity, Which can be extent, location, depth of burn, and contamination. If a burn becomes infected, it can go from a simple, non-scarring burn to a complex, deeper, scarring burn. When in doubt, see a doctor. Do not use butter on burns, regardless of size. Large-area burns, even if superficial, can become problems and should be seen.
Depends. A small burn can be addressed at home. If it is deep or covers a significant area of your skin, see an md, soon.