You don't find and deport them all at once. What you do is start enforcing existing laws against hiring illegals, and passing new ones using all the anti-illegal sentiment going around. Then, after a decent interval to give them a chance to get with the program, you start busting companies which don't comply. You can start with the easiest and most flagrant, and the biggest ones, like their token hit on Wal-Mart. You don't need a lot of busts and a big bureaucracy to do it, just move some of the migras from border duty to corporate policing. And finance the whole process with the fines you collect from the really big offenders. Publicize the busts so both the migrants and the American consumer get the message.

In the agricultural sector, you give them a year to clean up their act, and have the growers assist the migrants in getting the proper paperwork at the grower's expense, perhaps starting with a simple registration program and an ID card. They profit from cheap labor, they should pay part of the bill. Will the price of produce go up? Sure. It is artificially low now because of what we pay the migrants.

Very quickly, the word will get around in the business community that it is unprofitable to employ illegal labor and they will quickly make adjustments. As jobs get harder to get, the migrants will stop coming.
It will not happen overnight, so the shock to the economy will be bearable, and we will have time to set up programs to integrate the migrants we want to stay here and that will make good citizens.

The problem of illegal immigration is due to one fact and one fact only: Americans hire them. Until that is addressed, no walls or deportations or vigilante patrols will help, nothing will help.