When I play Black in 1.e4 e5 2.Bc4 on a Droid chess program, I do 2...Nf6 (recommended by de Firmian) and the program does Nf3 aiming to jump to 3...Ng5 and double attack f7. My brain is a little tired, but I don't see how to anticipate this trap while sticking with the recommended 2...Nf6. Please, tell me the obvious answer I'm missing. Thanks.

You can play 3. ... Nc6 and it will transpose to the Fried Liver Attack

Well, it'll traspose to the Two Knights defense, and after Ng5...d5, you're in the mainline there, which (even though I don't have the book you reference) I'm sure is what your author would suggest, rather than anything to do with the Fried Liver.

3...Nxe4 is also good, when you're going to end up in something more like a Petroff, and 4.Ng5 would just lose a knight.

Thanks to both of you. I had to scoot off to work. I'll try both these paths.

[I deleted comment after making an edit in original post]

After 1.e4 e5  2.Bc4 Nf6  3.Nf3 Nc6  4.Ng5,  you might want to consider 4... Bc5 - called the Wilkes-Barr or Traxler Defense.

Still, bear in mind that the Traxler can result in this:

Two Knights Defence, actually. It's only called the Fried Liver if all of the moves 4.Ng5 d5 5.exd5 Nxd5 6.Nxf7 happen next. There are plenty of good alternatives for both sides at several points, if those are played then it's not a Fried Liver.

Thanks to all. I'll explore these.

kwaloffer--I just noticed you are from Arnhem, Netherlands. Do people still do memorials at "the bridge too far"? What a story of "guts" (is this just an American idiom for great courage?)

Here's a nice study of the bishop opening with many traps.
https://lichess.org/study/17gfjLNM/woueIDBW