Endgame - up a minor piece

Hi, in the last couple of days I've played out two draws from won positions, one was a position I dominated the whole game, and the other a comeback win.

In both games I chose to dissolve material to take advantage of being a piece up and ended up being unable to make it count. Could someone give me an idea what I should be trying to achieve here?

I presume the idea is to send the king one way and the piece the other way, splitting the opposing king in two and then taking advantage of whichever side he chooses not to cover? but when to do this.

Also, did I dissolve the material at the correct time or should I have played on to make more of my advantage?

I've included two games, they're fully annotated, though not heavily, but feel free to skip to end game.

This is the game I dominated from the start, he wasn't ready for a Kings Gambit and surrendered  and early advantage, in all honesty I should have made him pay more and have myself to blame for not being more ruthless. However, I'm interested in the point from the Queen trade...

Game 1:

Tons of blunders from both sides! Ignoring that...

39. Nb3, collect the a-pawn and while the king is too busy stopping your a-pawn from promoting, take the rest of black's pawns and your h-pawn decides.

Interesting endgame though, where your knight cannot sac itself for black's a-pawn and must perpetually move as it is being chased. Thanks for sharing. 

Game 2:

Nice tactic!

34... Na2. Keep attacking those kingside pawns! It's an easy win. 35. Kd5 Nxb4 36. Kc5 Nd3+ 37. Kxb5 Nxf4 and no way you can lose. or you can sac the knight and connected pawns with 36... a6, where the a6 and b5 pawns are invulnerable to the lone king as they are connected passed pawns, and your king just mops up the kingside pawns and win.

Actually it was all going well. In fact, if you didnt know whether a h-pawn and knight wins, 46... g4 was smart and still winning, again due to connected passed pawns. To answer your question, his king can never step onto the fifth rank due to your g-pawn promoting. So, your king just pushes his king back slowly.

Hi again, From memory it was probably to hold the king pawn in position, I see what you mean though, it's better to just take the d pawn then attack then attack d4 with the bishop when the knight takes.

Thanks so much for the comments avatar_legend. In retrospect sharing the first game, although arriving at a similar endgame position, hasn't been that helpful maybe. I agree, it was blunder laden, from the start. I enjoyed messing around with the kings gambit but I think I'll save it for blitz games. Your comments on the second game were really helpful though, should perhaps have been going after the king side pawns first. A lot of it really comes from the fact I'm still a long way from being comfortable moving a knight about.

Thanks Bacon, I have heard of the rule where you trade pieces not pawns and it's something I'm going to have to read a little about and maybe look at Alekhines games. Totally agree with your comments regarding retreating, it was a hopeless move move by the bishop. Kinda seeing why people say you must practice the endgames to win chess now.