How to put up a newer political party

You don't need to "register" anything to form a political party.

The odds are stacked against new political parties, because in the late 19th and early 20th centuries, the Republicans and Democrats colluded to enshrine their own power, and to exclude challengers. However, a new party could be formed, although it would be expensive, difficult, and would take probably 20 years or more to get off the ground.

The first step is to organize from the bottom up. The history of politics in the United States is littered with examples of attempts to create political parties which were centered around an individual (John Quincy Adams, William Jennings Bryan, Ross Perot), or otherwise organized from the top down. For a political party to successfully organize and survive, it will have to be successful. In Perot's example, when he feuded with the Reform Party, he was in the position to sabotage them by withhold money--he spent as little of his own money as possible, and took as many legal donations as possible, but the money was donated to him as a candidate, and not the Reform Party because of any express ideology. Therefore, a new party would need to attract contributions. To do that, they would need to establish a track record as an organization which can get people elected. This will be almost impossible at the level of national elections because of the hundreds of millions of dollars necessary to run the Presidential, Senatorial and House elections. State elections are getting expensive, too--so the best option for a new party is to get established in many, many places, and to successfully elect people to local office, something which can be accomplished with small donations from party members and modest donations from a few wealthy supporters. Once a party has a proven track record for being well-enough organized to get people elected locally, they have a shot at attracting the kind of donations which can support state campaigns, and, eventually, national campaigns. That is why i say it would take at least 20 years, or longer. Such a plan cannot be organized from the top down, it needs to be a "grassroots" movement, and it needs to prove that the "grass" really has taken root, and will survive and prosper

The other significant factor is ideology. If your party can't tell me what is different, and better, about your party than either the Democrats or Republicans, why should i vote for you--especially as the Dems and Reps are proven "winners," while until you prove otherwise, your party will probably be seen as a loser. So you need to present an ideology which is attractive to a broad sector of the populace, and for which you can propose practical means of putting your agenda into operation. And it has to be something significantly different from what the Democrats and Republicans offer, because they're going to say "We already do that," and you're going to need to be able to say: "No you don't, and that's the problem"--and then prove that you're right.

Big project, and probably undoable, unless the Dems and Reps really screw the pooch.

I realized that i didn't really give you a satisfactory answer to the question of "registering" your party. I sometimes forget that i take for granted knowledge that may not immediately recommend itself to others.

You don't need necessarily to "register" a political party. You do need to get candidates on the ballot, and you do that with petitions. You'd have to gather the signatures of a sufficient number of registered votes, and be prepared to verify (at county boards of election) that the people who signed actually are registered voters. That would be in the beginning, when running for municipal and county offices. If your party survives and does well enough to run for state offices, you'd then need pockets deep enough to go to court to challenge the primary election system in any state in which you hoped to take high office, at which point you might be able to force the legislature (which is going to be controlled by Dems or Reps, who will close ranks to exclude you) to set up a primary election for your party, too.