In a typical divorce proceeding, both sides are required to provide a sworn statement of their finances, and to respond to written interrogatories, produce documents (e.g. financial statements made in loan applications, balance sheets, tax returns, bank statements, and copies of deeds and certificates of title and stock certificates) and be deposed in pre-trial discovery proceedings. Divorce lawyers have the authority to subpoena third-party records custodians and to take a small number of depositions of third-party witnesses prior to a permanent orders hearing and can usually get permission to take more if there is evidence suggesting that it would be fruitful to do so. There are a variety of sanctions that may be imposed for failure to cooperate, including adverse inferences regarding the facts that would have been disclosed if there had been disclosures in the discovery process. Still, it behooves a client to know as much as possible before commencing the process, since having lawyers gather this information during the course of divorce litigation is expensive and isn't always perfect.
Where misconduct is suspected, a spouse's lawyer will typically retain forensic accountants and/or private investigators and will compare bank and accounting and tax records with other public records such as real property records, corporate records and tax filings. Unless an asset has produced no income or expenses flowing through a personal or business account, it will usually show up somewhere. Spouses will also often have familiarity with where to look based upon living with a spouse and often will have obtained copies of relevant correspondence or documents to provide a lead - perhaps a letter asking a spouse to fill out corporate paperwork or receipt from a foreign bank account.
This investigation process (collectively called discovery) usually takes place between the filing for a divorce and the half year or more later when a permanent orders hearing is held. Often, in complex cases and cases where there is a likelihood that assets have been hidden, the final hearing will be set later after the original filing than it would otherwise be, and the planned hearing will be longer in light of the evidence that will need to be produced at that time.
In my state, a spouse has up to five years after a divorce to reopen a proceeding is undisclosed assets are discovered.
It isn't impossible to hide assets in a divorce, but it isn't easy either.