How to Deal With Players Who Want To Trade Everything?

Most of the time it will help you, because recapturing will tend to pull your pieces forward into the position while initiating trades removes a player's furthest advanced pieces.

But after something like 3 or 4 trades, it's reasonable to start avoiding them.

Also you can avoid any obviously undesirable trades like whatever your best minor piece is.

Also it depends on the position, but that's my basic advice i.e. you can ignore your opponent's bad habit unless the number of trades are getting excessive.

Just trade -- you'll be good

try to pull a tactic in one of your trades and gain +1 / +2 and go for the simplified endgame

Learn king pawn endgames. Learn about pawn structures.

Also I like to avoid trades (usually be retreating) when my opponent makes what I call a "single purpose move"

"Single purpose" meaning the knight or bishop is on a bad square, so the move only makes sense if they get to trade.

For example

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The starting position and end position are equal, so what was the big mistake?

The knight was badly placed on h5. If white simply retreats with a move like Be3, then black won't have anything better than going back to f6.

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Since both f4 and e3 are fine squares for white's bishop, the Nh5-f6 maneuver didn't do anything but lose a tempo.

I mean... I made the position very simple to better illustrate it. It's not like Nh5 loses or something. I'm just trying to show the concept... that if your opponent tries to trade by putting a piece on a bad square, and if you can retreat to an active square, then it's often good to retreat which will make their move look stupid.

The basic philosophy of trading a lot is an admission that they don't like tactical positions with lots of pieces on the board and prefer quieter positional play and/or are trying to make it to the endgame. Maybe try to do what they don't like and keep the position as sharp as possible. I know because I tend to trade too much just to simplify the position....guilty. When I resist trading I tend to do better. It's a defense mechanism because I'm old and tactics make my head hurt.

forks and skewers are typically a good way to get it to stop. The second you get any sort of serious material advantage, they are forced to stop going for trades and start looking for ways to gain back material.

I'd play Bg5 there. Then, not only is the N badly placed but the B is doing something useful on g5. White gains a tempo, whether black moves the Q or plays f6.

Its a very good chess forum topic and question.
Regarding players who try to exchange off all the pieces and pawns -
there's at least two situations possible there:
1) One is that they're putting so high a priority on such exchanges - that its making it easier or easy for you to beat them.
2) The other is that they're exchanging arbitrarily - but otherwise playing quite skillfully or skillfully enough.  Few or no blunders.  Or no obvious ones.
If that second type of player is also playing well positionally - then it will depend on your strength - as to whether you survive and win or can even draw.
'It depends on the position'.  
If somebody trades off your Queen - that doesn't mean you're going to win.  Not by itself.
When there's a lot of trading - it often ends in a draw.  

So - first point:  don't over-generalize.  You can't always 'take advantage'.

Related issues can come up when:
1) a player copies the other player's moves.
2) a player doggedly refuses to exchange anything - or bends himself/herself out of shape trying to avoid/prevent exchanges.

Objectivity pays:  In addition to:
"How do I justify exchanging here?"  (might or might not indicate bad thinking - that exchanges are to be avoided.  Doesn't follow.  Depends.)
there's
"How do I justify Not exchanging here?"

In tournament preparation - players are sometimes told:
"Keep pieces on the board - if you keep trading down and drawing then you're going to end up with half-points and finish out of the money"
But that's shallow.  
Too shallow.