Actually it is not at all difficult "find out" and to prove in court. I submit Exhibit 'A' - The Immigration Service's I-9 form. Every employer is required by law to have their employees submit a properly filled out I-9 in order to be eligible for employment. This document requires the applicant to supply documents to prove that they are permitted by the FedGov to work in this nation.
All it takes is for an INS agent to visit businesses that traditionally employ illegal aliens and simply demand to see the I-9's which must be on file and available. For every employee that does not have an I-9, the employer is fined. The INS agent then simply takes the remaining documents back to the office and performs whatever verification process that reveals the fraudulent from the honest. Those whose forms are not in compliance are brought to the employer's attention, and a match-up of forms to employee is made. For each hit, yet another fine is levied on the employer, and the employee can then be interviewed to see if that person is legal.
The procedure is rather simple, and in fact was implemented as part of a sting operation against some slaughterhouses in the north. The INS team was very successful in identifying the illegal workers and began to do what the INS, by law, is charged to do. That is when the complaints rolled in to congress, a few phone calls were made and the INS agent who came up with idea was reprimanded. Apparently the honest US citizen and legal alien must be forced to fill out an I-9 and supply the identification documents in order to be able to work in this allegedly "free" country, but the illegals and their benefactors are able to ignore this law and protect the privacy of the invaders.
So, my dear Pollyanna, the influx of criminals from all over the world will remain unabated because too many employers have discovered that illegal aliens don't complain to the authorities about working conditions or whether they are receiving minimum wage. Think about it next time you elect some jackal that promises to raise benefits and wages by force through the police powers of the state. What that congress critter is really saying is that they intend to increase the attractiveness of employing foreign labor.