It's a combination of "-te oku" (doing something with the regard to the future, http://www.guidetojapanese.org/learn/grammar/teform) and -tara (one of the conditionals, http://www.guidetojapanese.org/learn/grammar/conditionals). "いいですか" is asking for permission or approval etc., so you can determine the subject from this context.

何をしますか？ is What are "you" going to do? 何をしておいたらいいですか？ is What should "I" do? and this sentence is really polite.

For a study of grammar forms go here: http://www.guidetojapanese.org/learn/ The "~te oku/oita" form is used to avoid ambiguity in sentences like 何をしますか？ The form clearly marks "I" as the subject. See Lisa's examples.