When to swap material?

My understanding is that you want to swap material when you have a material advantage, when you're swapping for more valuable pieces, and when you'll have a positional advantage.  I'm not super clear on the last point.   Right now, I'm thinking about it in terms of not hanging any pieces.

What am I missing?

Thanks.

The Gotham Chess guy is always referring to bishops on certain colors, and while I realize it while playing, I never connected it to the pawn structure except at the end game when I'm trying to prevent a bishop from taking my pawns.  I did that in one game today, but I didn't think about it in the middle game.

Thanks again.

very early game, there is an investment factor.  If you moved your knight twice then let it get traded, you lost 2 moves for not much.    Consider also if attacking, does the opponent recapture with a pawn, and if so, is he stronger or weaker after?  Example... you trade and he takes making doubled pawns on the h file, this is probably weaker for him.  Example 2: you trade and he captures with a pawn that was already doubled, undoubling them and regaining a strong central pawn wall.  This is stronger than before, the trade may have been bad.   In a nutshell you trade to break an incoming attack, and avoid when attacking yourself.  You trade to simplify to a winning endgame, so how the pawns and pieces fall out after is critical to do or not do the trades.   You trade to make their position worse or break an attack or because you have a winning plan afterwards.  Hard to see these, but you will in time. 

Trades come with experience. As you learn to recognise good and bad pieces you'll try to trade your bad ones for your opponents good ones etc. One way to look at it is what are the prospects in the position for the pieces which is dictated by the pawn structure. So there are good and bad bishops. Then closed positions favour knights and open positions favour bishops which might influence your trades or whether you open the position or keep it closed. Then there is removing defenders, so if your opponent has a weak pawn you want to attack on a dark square, your LSB wont help in the attack but might be used to remove a defender such as a knight. If there is a great weak square on the 6th rank that you want as a knight outpost, trading off your opponents bishop of the same colour will help further weaken it by removing a defender. Playing through annotated GM games is a good way to pick this stuff up, and books on the middlegame, planning and strategy.

If the opponent's piece is much more active than your own, offering a trade might force a concession out of your opponent... either he trades off his nice active piece for your less active one; or he declines the trade and retreats it, so that you gain some activity at his expense.

A typical pattern I see is a knight defending the king with the bishop being the most obvious approach to remove the defender.  Sometimes I can get a pawn to do the removal, but it's far easier for me to sacrifice the bishop for the knight.  But I haven't quite gotten down the timing as I can usually do this really early in the game.  Usually, this ends up being a knight pinning the queen.  If I take the bishop, I open the position, so that the queen can move.

I see this on Gotham Chess too, where the defense is to push two kingside pawns to force the bishop to retreat.  In this particular situation, I'm trying to figure out the timing.  I'd rather exchange the bishop for a knight than lose it to a pawn or another knight.

The good thing is that similar patterns present themselves over and over again.

Pushing the K-side Pawns to force the Bishop back can be quite double-edged, though.

Some reasons to trade I guess. Trade based on piece activity. Moving a piece away from a square. Bishop trades depending on pawn structures. Removing a defender of key squares or pieces. Open up lines to the king. Simplification while ahead. Weaken their pawn structure. These are some of the positional advantages you can get from trades.

Yeah. Pushing the h pawn (putting the question to the bishop) can be weakening and may invite a pawn storm. The knights on f3 and c3 help control the central squares e4/5 and d4/5. Pinning or capturing them removes them as defenders of the centre, allowing the other side to grab a pawn or centralise a knight, so it can be useful to think about those exchanges in terms of central control. If you have no plans to take advantage of the central squares controlled by the knight, consider whether it is worth the exchange.

In your example, white gives up kingside castling to defend their bishop.  The moment they push the pawn to defend their bishop I'm thinking that they'll either queenside castle or not at all.  

What I don't get in your example is: why doesn't the knight pull back to the eighth rank (c8) to avoid the pawn?  Then if they push the pawn, you can take it with another pawn and open up the rank with your rook.  If you pull it back, it will be defended by the rook, rather than hanging on the loose.  And you're still up material only losing a pawn to take a bishop and a pawn and a potential open file for your rook.

c8? Do you mean e8?

On 8. ... Ne8 9. Nxe5 (threatening Qh5 and mate) looks like the end of the world.

Remember that the Bishop on c4 pins the f7-Pawn against Black's King, so your idea that " Then if they push the pawn, you can take it with another pawn and open up the rank with your rook. " doesn't work anyway.

Once the knight is no longer protecting the pawn in your example, you can take with the queen, which would prevent the queen move in your new example.

You mean like this?

In any case, the point that I was making (in post #8 above) was that pushing the K-side Pawns after you've castled on that side is very risky. It's much less risky to push Pawns on the side opposite your castled position... as in the Ruy Lopez, where Black often castles K-side and plays a6 and b5 (on the Q-side) to drive away White's light-squared Bishop.