How to combat this type of opening.

The main defense is Nf6.  That blocks the Queen's access to f7, which is the point behind people playing this opening.

I found a game that I played in 1973 against a player with a USCF rating of about 1400.

1 e4 e5
2 Bc4 Nf6
3 Qf3  

This move is wrong on two counts: it brings the Queen out too early, where it is subject to attack by one or more of Black's minor pieces, and 2) It robs the Kings Knight of its best square.  It also pulls the Queen off of its protection of an eventual d4.  At f3, the Queen is threatening nothing, unless Black is foolish enough to move the Knight from f6.  It's not only a wasted move, but it will result in at least one more wasted move if and when Black plays Bg4.

When I asked the man why he played the move, he said that he wasn't watching, having thought that I'd played 2 ... Bc5, as that's what the players he usually played against did.

3 ... Nc6

Black proceeds with his development and already has the unpleasant threat of Nd4

4 Nc3?

Better would be either c3 or Ne2, both of which stop Black's next move.

4 ... Nd4!

Normally it's not a good idea to move a piece twice before developing others, but it's good in this case; Black has a tactical shot here.  With the given move, Black threatens both the Queen and the pawn on c2, which forces White to move the Queen back to where it came from.

5 Qd1

White has now moved the Queen twice, only to find it on the square it started on.  Black has two pieces developed to White's one AND has the move.

5 ... Nxe4!

The tactical shot mentioned.  Black seems to waste time moving the other Knight again as well, but he'll get the time back with interest later.

6 Nxe4 

6 Bxf7+ looks good, but after Kxf7, 7 Nxe4 d5!, White's Knight has to move away and Black controls the center, has the f-file open for his Rook, is ahead in developmen,t and has avenues open for both Bishops; much more than enough compensation for the slightly misplaced King, which will be able to go to g1 after the Rook is moved to f8.

6 ... d4
7 Bxd5?!

Better are either c3 or Bd3

7 ...  Qxd5

Threatening the Knight and indirectly threatening the g-pawn behind it and the Rook behind that.

8 d3?

A better idea was 8 f3, which would have stopped White's veiled threat of Qxg2 and given the Knight f2 to retreat to after the move in the game.

8 ... f4!

When you have the advantage, don't be afraid to be aggressive.

9 Qh5+

Not much better is 9 Ng3, which protects the Rook, but after 9 ... Qxg2,10 c3 Nc6, 11 Nf3 f4!, 12 Rg1 Qh6, 13 Ng5 Qxh2, 14 Nf3 Qh6, 15 Ne4 Bf5, White would be down two pawns, with no compensation.

9 ... Kd7!

My opponent was hoping for 9 ... g6? 10 Nf6+, which gives him a better game than he got.

10 c4 Qa5+

Better for me would have been 10 ... Qg8! 

11 Bd2 Bb4
12  Qf7+ 

The problem here is that White has no other pieces out except the Knight, which is under attack, and therefore nothing to help the Queen.

12 ... Kc6
13  Nc3 Be6

Black gets the Bishop out with tempo and connects the Rooks, before going after White's Rook on a1.  I wasn't worried about the g-pawn here, since it can't be saved anyway without wasting valuable time.

14 Qxg7 Rhg8

I didn't like the immediate 14 ... Nc2+, 15 Kg1 Nxa1, 16 Nf3, threatening the pawn on e5 and starting an attack against my King.

15 Qxh7

15 Qh6 might have been a bit better.

15 ... Nc2+
16 Ke2 e4!

Played after 30 minutes of thought.  16 ... Nxa1, 17 Nf3 Nc2, 18 Nb5 cuts off communication between Black's Queen and e-pawn and threatens to mount an attack.  The given move keeps the pressure on and temporarily keeps White's King's Knight from reaching its best square.  

17 Rc1

Better would have been 17 Qh6 Qe5, 18 Rc1, which pins the Bishop and gets Black's Queen out of White's hair on the Queenside.

17 ... exd3+
18  Kd1

Played after about 20 minutes of thought.  White correctly avoids the pawn, as 18 Kxd3 Bxc3, 19 Bxc3 Qa4! leaves White's king exposed to attack from many points.

18 ... Bxc4
19  Nf3

Queen checks only drive Black's King to a safer haven, i.e. 19 Qh6+ Kd7, 20 Qh7+ Kc8.

20  ... Rae8

Stopping the Knight from checking at e5

21 a3

Probably better is to just give up the Rook for the Knight and pawn then and there with 21 Rxc2 dxc2+, 22 Kxc2 Rxg2, but Black is up the Exchange then.

21 ... Bxc3
22 Bxc3 Qd5
23 Rxc2

White has to do this before Black can reinforce the Knight with Bb3

23 .... dxc2+
24 Kxc2 b6

Black makes room for his King to flee into the safety of the pawns

25 Nd4+ Kb7
26 Kc1

A good move, played after about 15 minutes of thought (I know this because I annotated the scoresheets with all lengthy time spent on moves).  White prepares for Rd1, which isn't possible here because of Black's threat of Bb3+

26 ... Rxg2
27 Qxf5 

The best of a bad lot.  Black needs to neutralize White's attack if he is to have a game to play, and getting rid of the Queens is a good way to slow down an attack.

27 ... Rxf2
28 Ng3 Bd3

Cutting off the King's flight to the safety of the corner.

29 Bd2

Stopping the Rook's check at c2, although such a check wasn't dangerous at the time.    The next five moves contained minor errors for both sides, but Black has a won position anyway.

29 ...  Rh8
30 h4 Rg2
31 Bf4  Rf8
32 Be5 Rc2+
33 Kd1  Rd8
34 Bf6  Rd6!

Black  doesn't give White time to move the King to e1.  With this move, Black wins material.

35 Be5 Rd5
36 Bf4?!

My opponent was in time trouble; he only had 2 minutes left for the next 5 moves.  He allows a mate in six, but he had to lose material with anything else.

36... Be5+
37 Ke1 Bf3!

I was in time trouble myself, having about a minute  for the next 4 moves, and I didn't see the mate ahead, but I could see that the only way that Black could stop mate at d1 was to give up both minor pieces. 

38 Bd2 Rdxd2
39 Ne2 Rxe2+
40 Kd1 Rh2+
41 Ke1 Rc1#

 At which point, White performed the castling maneuver (which of course was illegal), then shook hands with me and went up to the scoretable to tell the tournament director the result.