によって, による, and により are all different versions of the same expression, that can basically be translated as ‘according to (A)’, or ‘depending on (A)’. This uses the same よる as seen in the grammar pattern によると. They will be used in the following way:
によって - Generally used before a comma (although not always). Acts as the separation point between the (A) and (B) parts of a sentence. Made up of the 格助詞（かくじょし） (case marking particle) に, and the う - Verb よる in its て form.
による - Generally used at the end of a sentence, to highlight that the previous statement depends on (A).
により - Almost always used before a comma. Acts as the separation point between the (A) and (B) parts of a sentence. Made up of the 格助詞（かくじょし） (case marking particle) に, and the う - Verb よる in its 連用形（れんようけい） (conjunctive form).
To use any of these constructions, attach them to the end of a noun that you want to express as being the ‘dependent’ thing.

• 地域（ちいき）によって、ゴミ出（だ）しルールが違（ちが）う。
  Depending on the area, the rules for throwing out garbage are different.
• 行（い）けるか行（い）けないかは休（やす）みが取（と）れるか取（と）れないかによる。
  Whether I can go or not depends on if I can take a day off.
• ベンおじさんは強盗（ごうとう）により、命（いのち）を奪（うば）われた。
  Uncle Ben's life was taken by a robber.