Actually, it would be quite simple.
Just make it illegal to employ anyone who is not in the country legally, either formally or informally, AND ENFORCE THAT LAW. Send violators to jail and issue hefty fines to them and their employers. Second, prohibit any benefits of our "safety net" from going to people who are not in the country legally, including public schools, SNAP benefits, Medicaid, housing subsidies, and so on. AND ENFORCE IT.
Then offer transportation assistance to get the people back to any country where they can legally reside.
Should the problem arise of "people doing work that Americans won't do," increase the scope of guest worker laws while making it illegal for guest workers to bring their families, and requiring a fixed date by which they must return to their home countries, respectively.
As icing on the cake, impose an immediate 5% assessment on all funds transferred from foreign nationals in the U.S. to their home countries. Maybe Trump could thereby get "Mexico" to pay for the ******* wall.
Cancel anything relating to "Dreamers," who are in fact illegal aliens, and treat them just as you would any other illegal alien.
Really, it wouldn't be that difficult.