I use PyChess to play. It talks sometimes about how White or Black moved their pawns into "stonewall formation."
How do they do that, and what are the position's advantages/disadvantages?
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Black usually reaches the Stonewall formation from the Dutch Defense (though QGD is an option as well, if he/she postpones Nf6) and involves putting pawns on c6, d5, e6 and f5. These pawns guarantee a strong grip on the light squares in the center (especially e4, which is often occupied by a knight later on), but weaken the dark squares. Another problem for Black is the light-squared bishop, which is severely limited by its own pawns. A typical Stonewall position is the following:
[FEN ""] 1. d4 f5 2. g3 Nf6 3. Bg2 e6 4. Nf3 Be7 5. O-O O-O 6. c4 d5 7. Nc3 c6
It's hard for White to crack Black's center, but he has many options, of which my favourite is to exchange some pieces and take advantage of Black's bad bishop in the late middlegame and endgame.
As @user1583209 notes, if White tries to reach this formation it's called the Stonewall Attack – see the linked question for more details.
The stonewall setup results in Black putting their pawns on f5, e6, d5, and c6. White could also play the setup by putting his pawns on c3, d4, e3, and f4. In the rest of this post I will assume "Black" is the person playing the stonewall.
The Stonewall's idea is to close the center and gain attacking chances on the Kingside. Due to its closed nature, the side playing the Stonewall has the opportunity to take their time developing and creating a plan.
The main drawback of the Stonewall is the big gap in the middle of the board on e5 created by the f5 and d5 pawns (assuming Black plays it). This nuance usually gives White an advantage, as it is a very good outpost for one of the Knights. This can be especially dangerous if White begins an attack on the Queenside, since the Knight on e5 is in a perfect position to target the c6 pawn. If White pushes his b-pawn to b5 and has a Rook on the c-file, the c6 pawn will be under an unbearable amount of attack. This is why it is vital for Black to begin his Kingside attack quickly, lest he be overwhelmed by White's positional advantages.
It's a dynamic opening that is a bit risky and slightly dubious, but if you play it right it can lead to some very exciting positions.
Here is a link to an article of two chess Grandmasters discussing the Stonewall setup:
If you would like to look at some games that feature the Stonewall setup in them, here is a good link for that:
For further information on the Stonewall, I would highly recommend looking up some videos of Grandmaster Simon Williams explaining it. He's one of the world's foremost experts on the Stonewall and has written some very good books on it.
Hope that helps.
The one shown above is the more modern approach. The classic stonewall develops as f5/nf6/e6/d5/c6/Bd6 with Qe7/Qe8 ideas. White's Bg2 is biting on granite.
The stonewall is very simple to play strategically for Black. Most white players "scoff" at it when you play, but eventually, after they are tipping their king, learn to respect it.