What is this common opening called?

I keep seeing opponents run something like

• e4
• d4
• Nf3
• Nc3

So the middle 2 pawns are forward 2 spaces and they are covered by knights.  Sometimes the bishops also step in front of king and queen.

What is this structure called?  If I know the name, I'm sure I can find threads on attacking it.

What about black's moves? 

It's not an opening unless you know the moves of each side.

It can be a system, but I don't believe this system has a name.

get chesspad.

edit a free software that contain every opening's name(EcO)

 so you can check the opening name by moving the pieces.

My moves as black are usually with the intent to quickly get to a king-side castle.  This diagram is one example.

But I've seen both white and black set up the structure that I've illustrated with white.  Does it have a name?

In your example, white played normal developing moves, and black played trash.

Whatever name you may have heard it referred to a position where both sides played reasonable moves.

So ... would a memorized opening help me play something other than "trash"?  My rating's been slowly improving even with opening moves like these.  Would something more sophisticated be a big step forward?

You should avoid moving your pawn on g6 forward if you don't intend to place your bishop on g7. That is the normal purpose of weaking the king side pawn structure to add a bishop that has "cover" by the pawns. If the bishop isn't there then you have weakened your king side pawns for no strength to their position. Also the bishops usually shouldn't be in front of your center pawns as the center pawns normally need to be thrust forward to gain space and contest the valuable central squares.

If I were you I'd either read up and learn the principles of opening moves or look for several opening lines to begin learning that are "time tested", meaning reliable openings that have been used by chess players for decades. You'll get better results than you do now and over the long term I assure you. I could help you find some if you'd like.

OK, thanks to all of you.  I'm looking again at the "book openings" at http://www.chess.com/openings/

I'll pick one and start trying it in my next few games.

Suggestions are welcome!

I would look to play openings with a variety of position types. For example I may play the King's Gambit as white if black plays 1.e5 to my 1.e4 or if black plays 1.e6 instead I may opt for a more closed King's Indian Attack. With black I may play the Sicilian Defense against 1.e4 and the Queen's Gambit declined against 1.d4. If you have a variety of different types of openings that gives you a mix of different kind of positions with different pawn structures you'll learn more and eventually when you are a stronger player be able to determine if you prefer closed or open positions and then tailor your openings to that type.

 By tucking my bishup into g7, does this become "Modern Defense" -- and a better opening?

It is better with the Bishop on g7, but now there is a hole in Black's position on f6. This may not be fatal, but it's more usual to play d6 than e6 in this sort of position. I don't play the Modern, and Black may be able to get away with this kind of play; if Black can play f5 he solves this problem, and maybe eventually s/he can out of this position though at the moment it just looks like the Kingside is needlessly weak; someone else might be better suited to speak to this. In general I do think it's often said that "g6 and e6 don't mix."

I'm not sure because when I play against that black setup I don't often put a knight on f3.

We get people on here who obsess about opening names/lines and you end up not reacting to your opponents plans because you're set on where you want your pieces.

Do as Firebrand says and learn about centre control, tempo etc, not lines/names.

The other thing about e6 and g6 is both of them are plays to free up the dark squared Bishop, and you only need one. Another reason d6 is played more often is it opens up the Light-squared Bishop. In your diagram that Bishop is entomed by pawns on e7 and d6... by contrast in mainline Moderns and Pircs (as I understand) d6 is favored and the Bishops can work well to put pressure on d4... ie one Bishop g7 hits d4 and the other might someday come to g4 pinning the knight (one of the defenders of the d4 pawn.) If you look at the wiki for the Modern Defense you'll see Black tends to play g6, d6, and not e6. http://en.wikipedia.org/wiki/Modern_Defense http://en.wikipedia.org/wiki/Pirc_Defence like others are saying it's not important which you play and what it's called, but if you understand what I was trying to say about the f6 square and the d4 maybe you can understand why d6 might be a better move than e6 (although it's possible e6 could work too if Black can push the f-pawn later; I don't know; it looks risky.)

an early e6 and g6 together severely weakens the dark squares around black's kingside.

i often get very quick wins with an early 4 h4 (instead of Nf3), though my opponents usually aren't very good players - but if they were, they wouldn't be playing this to begin with, so it's not very fair.

isnt it 2 knights opening??

That pretty much sums it up.

The name of the opening where White can play e4/d4/Nc3/Nf3 unchallenged is "Black's cluelessness".

my time to be an openings zealot and say that you are insulting the Modern Defence. :P

With all the hate and disrespect I have for the modern, I have to admit that the modern defense does not fill the "unchallenged" criterion.

neither does g6 Bg7 e6 Ne7 - but yeah, it's tough to characterize systems where both sides have so many options :P