hello derek,
the best way to encounter the philidor is to avoid it: play the king´s gambit
My second choice (and admittedly a practical one) is to play 1.e4 e5 2.Nf3 d6 3.Nc3 with 4.g3/5.Bg2/6.0-0/7.h3 to follow. Then later you can open the game with d2-d4 or attack on the kingside with d2-d3/Nf3-h4/f2-f4 . It´s a kind of KingsIndianAttack or Fianchetto Pirc or Four Knights Glek Variation (however you want to call it). Many Philidor players are unfimiliar with this as they cannot exchange quickly on d4 and attack the pawn on e4.
After 3.Nc3 f5!? there is 4.d4 fxe4 5.Nxe5?! Nf6 6.Bg5 dxe5 7.dxe5 Qxd1+ 8.Rxd1 with compensation for the piece. This is in fact a sideline of the latvian gambit (1.e4 e5 2.Nf3 f5 3.d4 fxe4 4.Nxe5 Nf6 5.Nc3 ...) and I don´t know if it is refuted, in blitz games it works fantasticly!
If you really want to improve you should play the principal and main line with 1.e4 e5 2.Nf3 d6 3.d4! though it´s some theory to learn and black players usually know their stuff. But white should get a slight advantage in an open game.
It´s not easy to continue in variations as black now has a wide choice:
(a) 3...Nd7
(b) 3...exd4 4.Nxd4 g6
(c) 3...exd4 4.Nxd4 Nf6 5.Nc3 Be7
(d) 3...exd4 4.Qxd4 Nc6 5.Bb5 ->Ruy Lopez Steinitz
(e) 3...exd4 4.Qxd4 Nf6
(f) 3...Nf6
(g) 3...Qe7?!
(h) 3...Bg4 4.dxe5 Nd7?!
I suppose your friend plays an Hanham like (a) with c6/Qc7/Be7/Nf6/0-0 to follow. But after 4.Bc4! you have real threats against f7, for example 4...Be7? 5.dxe5 Nxe5 6.Nxe5 dxe5 7.Qh5 +- . I cannot give the whole variations here but in every line white should keep advantage. (f) is a try to improve with 3...Nf6 4.Nc3 Nbd7 as Nf6 is more important for black´s development than Nc3 for white. But 3...Nf6 4.dxe5 is a little better for white. (g) should not bother you, what do you play against 2...Qe7?. (h) is an unsound but dangerous gambit.
I don´t know the 3...exd4 lines very well (as I play 3.Nc3 , see above), maybe someone else can help you!?
(c) seems to be the modern main line and is played by GM Bacrot.
Against 1.e4 e5 2.d3 a natural development with Nf6/Nc6/d5/Bc5/a5/0-0/Re8 is good for black, a sharper try is 2...Nc6 and 3...f5 .
I hope this was a helpfully first introduction!?
tracke