In the most recent episode of the Ricochet Podcast, Reince Priebus talks about the need to create a permanent party infrastructure in minority communities. I defer to his expertise on the specifically political, but one idea I've had is for the party to establish a non-profit that would open American Opportunity Centers around the country to teach immigrants English and history/civics. This could be something for local party volunteers to do when there's no calls to make or doors to knock on, and it wouldn't necessarily be expensive (it would certainly cost less than the $400 million Karl Rove flushed down the toilet last year).
While there wouldn't be any campaigning or even anything overtly political at the Opportunity Centers, they would clearly be identified as a Republican project and would provide something that's in great demand among newcomers. In fact, in addition to language instruction and studying for the citizenship test, the Opportunity Centers could also have workshops on how to start a small business (helping them navigate the maze of red tape crated by the leftists), and maybe other subjects, like how to establish a good credit record so you can apply for a mortgage.
Would alumni of the Opportunity Centers who passed their citizenship test end up mostly voting Democrat? Probably, but that's going to happen anyway (which is one of the myriad reasons future immigration has to be reduced), but the Opportunity Centers would help make it more likely that the minority of immigrants who are open to the conservative small government message actually hear it.
Even more important, Opportunity Centers would connect grassroots Republican activists to immigrants, allowing each to see the other as they really are, rather than as the media or chauvinist groups like La Raza portray them.
I've been teaching citizenship classes for some time now in the DC area at a fine operation run by Catholic Charities and have benefited a lot, and, I hope, helped some of my students. If Republicans want to do a better job at connecting with future Americans, they need to do something real like this, not pander with a Spanish response to the State of the Union or play me-too politics by backing the left's amnesty schemes.