After all the investor hubbub over the oh-no-they-didn’t deal between Yahoo and Microsoft starts to die down a bit, the pair are now embarking on the path that is the only way toward proving the efficacy of them joining together.

That would be getting a variety of state, federal and international regulators to say yes to the wide-ranging online advertising and search arrangement they announced last week so they can start making it work.

According to sources at both companies, a variety of filings will be made this week, including one to the Securities and Exchange Commission that should provide more details of the partnership.

When it was unveiled last Wednesday, the companies said Microsoft (MSFT) will run search technology for the two, while Yahoo (YHOO) will sell the premium search advertising.

That SEC filing could answer a number of questions some still have about the deal, such as whether there is a large break-up fee that Microsoft would pay Yahoo in case the deal is scuttled.

That’s just the outcome that Microsoft and Yahoo are trying to avoid.

“We think of it as an outreach effort to explain how we are creating a strong No. 2 to Google,” said one source close to the situation. “The main goal will be to show that a better competitor in the marketplace is a good thing.”

While the companies are prepping for opposition from Google (GOOG), sources close to the thinking at the dominant search company said it is more likely to be muted and indirect.

That’s especially true since a MicroHoo makes Google–currently under a lot more government scrutiny than ever before–look like less of a bully.

Thus, Google’s tactics would entail less direct statements and more pointing out the discrepancies between what Microsoft said when Google tried to get approval for a search deal with Yahoo last year and what it argues now.

“They will probably not be that obvious, but they will be there still,” said Microsoft CEO Steve Ballmer to me, in an off-hand remark at the software giant’s Financial Analyst Meeting last week.

It’s a game of legal chicken that Ballmer knows well.

Already, for example, Microsoft and Yahoo execs have been aggressively reaching out to major publishers and advertisers to get their staunch support.

That included calls immediately after the deal was announced last Wednesday to such execs as Martin Sorrell of the WPP Group (WPPGY) and Jeff Zucker, CEO of NBC Universal, a unit of GE (GE).

In Washington, D.C., both companies have legions of lawyers to try to make sure the Justice Department, which will review the case due to its antitrust implications, has all the information it might need.

And, more to the point, they want to avoid the debacle that took place when Yahoo and Google tried to get approval for their failed deal last year.

That deal was ended by Google after it became clear that Justice was going to fight it by arguing that top search companies hooking up hurt competition and stifled innovation.

In addition, there might be Congressional scrutiny, with possible hearings, similar to those held when the Yahoogle deal was pending, such as in the Senate Judiciary Antitrust Subcommittee.

And, of course, there are actually independent groups concerned and they have also been in contact with regulators.

“There are questions that must be answered regarding the collection and sharing of consumer data by the two companies,” said Jeff Chester, executive director of the Center for Digital Democracy, a D.C.-based group that works to promote consumer privacy and protection online, in a statement last week. “While the rationale for the deal is to provide some much needed competition to Google (and income for Yahoo), the further consolidation of the global digital advertising system should be a concern to Internet users, privacy advocates, online marketers, and competition regulators.”

Sources said Microsoft and Yahoo also plan to petition regulators in the European Union this week, which is likely to be most concerned about privacy issues involved in their union.

They will also be doing the same in other key countries worldwide, such as Korea, Taiwan and Brazil.

And, finally, given how involved state attorneys general became in beaching the Yahoo deal to partner with Google, they also will be starting outreach to key states, such as California, where Silicon Valley-based Yahoo is headquartered.

“Once again, it will be the Lawyer Employment Act of 2009,” joked one person close to the deal. “At least, that shows there is some economic benefit to this deal already.”

While we all wait in breathless regulatory anticipation, here are interviews I did at last year’s Senate hearings on Yahoogle, with lawyers from Google (David Drummond), Microsoft (Brad Smith) and Yahoo (Mike Callahan).

Incredibly, they are the very same lawyers who will be pretzeling themselves in entirely different shapes than they pretzeled themselves a year ago.

I would expect nothing less!

Here’s the video: