Oxygen is used by the yeast in the early stages to reproduce. So before (or at the same time) you add yeast, you should aerate the wort. A good shaking, or a whisk works well. Once you think you have aerated enough, you should repeat it. Just pouring into the fermenter adds some O2.
Dry yeast suppliers say you don't need to aerate, and the yeast itself has everything it needs, but I would still aerate.
You do NOT need to use Oxygen. For a beginner, aerating the wort is sufficient. On high gravity beers 10%+, pure O2 will help as you need to maximize the yeast, but for most beers the difference between a decent aeration of the wort and pure O2 is minimal (maybe .001 on FG).
And yes, after the first 24 hours aeration/O2 is bad.