What would a third party need to do to win national elections

Well, the problem is that the current parties running, such as the U.S.A.'s Republicans and Democrats, are already so large people are afraid of voting for something else.

Suppose, for example, that you really wanted the Independent party to win, so you vote for them obviously. Unfortunately, not enough people voted for the independent party, so the party lost. About 13% of the normal Democratic supporters did the same thing. Due to this, neither the Independents nor the Democrats won. Next year, you imagine the same thing will happen.

Now suppose that you really didn't want the Republicans to win. You don't really want the Democrats to win either, but you really want to make sure the Republicans stay out of power. Since you know that it is very unlikely that the Independents will win, you decide to vote Democrat because you want your vote to count, and you know that the Independents won't win.

As more and more people fall into this line of thinking, more and more people will just vote for the original two parties, meaning that the third party will continue to lose, meaning that more and more people will vote for the original two parties. It just keeps going around and around.

As far as I see it, the only real way for a third party to win the National Elections if if both of the original parties fail in such a spectacular way that enough people decide to go against the norm and vote for a different party.

Of course, a change in the voting system to remove the fear of your vote not counting can also help.
Hope this helps :)