How to prove that I entered the US illegally?

In order to apply for a work permit under the Deferred Action for Child Arrivals process, you need to provide evidence that you entered the country before your 16th birthday.  This is fairly straightforward if you entered the United States legally (that is, after inspection by an immigration agent) because most likely you will have a stamp in your passport and Form I-94 would be attached to the page where the stamp was put.  Both of these are solid evidence of your entry into the country.

However, if you have lost the passport and/or Form I-94 or you entered without inspection (you simply crossed the border illegally), it gets tricky.  You will now need to rely on other forms of evidence to demonstrate that you were in the United States.  For example, the USCIS is saying that evidence of your attending a high school or receiving medical treatment at a US hospital can be used instead.  Maybe you still have a copy of your itinerary from the airline that you boarded to enter the country.  These are some of the examples that can give you an idea about what to present as documentary evidence of your presence in the country.