According to multiple sources, and using different methods of checking it, about 20-30 million - and the higher number is likelier to be more accurate.
I found information about the OFFICIAL number (12 million), and why many dispute that number, in Ann Coulter's Adios Amigos book.
But, I'm not one to just blindly accept other people's numbers, so I did some checking.
The Wall Street Journal - almost unique among newspapers for having reporters who actually understand numbers - says that EITHER set of numbers is, at best, only a rough guess (for various reasons, including the fact that the US census doesn't even ASK about immigration status!).
Justich and Ng, at that time researchers for Bear Stearns, came up with the highest numbers, using a variety of means:
Bear Stearns' conclusion of dramatic underreporting was calculated by analyzing various data not included in other reports: border crossings, foreign remittances, housing permits, school enrollments, demand for language proficiency programs and service demand in gateway communities for illegals – all of which lead to findings contrary to Census Bureau numbers.
Keep in mind that the Bear Stearns report depended on hard numbers, not directly tied to sources that had a bias towards under- or over-counting.
I took a course in college on Civil War and Reconstruction. For that class, we had to create a history of a single unit - either North or South. For most of us, it was our first experience using original sources.
One major problem for most of us is that the evidence contradicted itself, depending on which source you consulted. I remember asking, "If both sides indicate that the battle took out hundreds of the enemy, and only a few of their own, who do we believe?"
His answer: Look to the next-day muster - units report who is still standing, and will get a paycheck.
In other words, as the Watergate investigators found, look for the money.
On those grounds, the Bear Stearns data is probably better than most, as it relies on remittances, specific targeted requests for services, and similar information sources.
Ann Coulter estimates that about 1/4 of Mexico is currently residing in the USA.