I will repeat, if you really wish to improve your game and you are down a piece in anotherwise equal position--resign!
Better to play another game and try to learn not to be down a piece in the first place and/or improve your tactics so as to not be down the piece in the first place.
If you are playing "for fun" and are not so inclined to improving your chess play and you are down a piece then avoid most trades--pawn or piece.
If you are down a minor piece then you need to trade pawns equally to activate your pieces that you have left so they are stronger and also so that any extra material that your opponent has in the end game will not be enough to Force mate. If you are down a pawn or two then unless you have a great position with your pieces and or better development so that you can attack your opponent successfully then you need to trade pieces to create an endgame with a little bit of material on the board and some pawns. the idea is that you do not want your opponent to have enough material active to attack you and at the same time you want to make it hard for your opponent to be able to make any progress. Also if you are down a minor piece and your opponent has a past Pawn that cannot be stopped from queening then of course the strategy of trading Pawns has to be put off until that settled .