In general, the citizen must witness the misdemeanor being committed.
In the case of illegal immigration, the citizen would have to see the guy cross the border illegally.
Tell the person, "You are under citizens arrest",
take control of the person, ask the person if "they have any weapons or sharp objects on their person?
tell the person "For your safety and mine, I need to do a pat down, search".
Now, you need to take the person to or call the cops to take custody from you. A state trooper will do.
If you don't want to confront the person, then you can report him or her to the police, who will then take the person into custody.
http://www.leginfo.ca.gov/calaw.html
* 207-210 kidnapping
* 210.5 false imprisonment
* 236-237 false imprisonment and human trafficking
* 833-851 arrest
* 853.6-853.85 arrested for misdemeanor - notice to appear
* 13519.4 racial profiling
United States Attorneys' Manual
http://www.usdoj.gov/usao/eousa/foia_reading_room/usam/
1907 Title 8, U_S_C_ 1324(a) Offenses
1908 Unlawful Employment of Aliens -- Criminal Penalties
1917 Arrest, Search, and Seizure by Immigration Officers
1918 Arrest of Illegal Aliens by State and Local Officers
2056 Preparation of Witnesses Whose Testimony May Involve Classified Information
United States Code http://www.gpoaccess.gov/uscode/
8USC1101 Foreign worker defined
8USC1304 Forms for registration and fingerprinting
8USC1306 Penalties
8USC1325 Improper entry by an alien
10USC906 Spies
18USC2381 Treason
50USC21 Enemy Aliens