In many of my recent games, I've achieved excellent positions out of the opening and middlegame against expert and master level opposition but failed to convert any of the positions for a win.  I'm not going to post full continuations here, but it's becoming clear that although my positional understanding is strong enough to reach advantageous positions, I lack the extra push required to finish out a game.  Looking at the below positions, can a strong player tell me how they would go about winning the below positions?  I'm not looking for concrete variations, just ideas for realizing the advantage in the position without allowing counterplay or drawing chances.

Im not really sure of how to continue the 1st game. How abt h3 followed by Bh5 (1st game) But for the 2nd game, whites king looks pretty open without the f pawn. So i will suggest 28... dxc3 29 Qc3 Qc5+ 30 Rf2 Rd2 31 Rcf1 32 Rd1! with some good play. 

In Game #1, you first need to play a move like a3, allowing an escape square for your king. From there, I would try to trade off the queenside pawns and try to hold a draw. This position is likely to be winning for black, based on 3 factors.

A) Piece Activity - Yes, white's queen looks nice, but really all you are doing is using a 9-point piece to hold a 3-point piece where it is. Looking at the bishops, they have no scope.

B) King Safety - Your king is actually facing some problems. To start, it will need a place to hide, or else a bishop will have to guard it. If the king goes to h3, then the g3-bishop is stuck in its place.

C) Pawn Structure - Your d5-pawn is very weak, and I expect it will be hard to hold on to. After that, black's pawns will come rolling like an avalanche.

Conclusion: If you were able to draw this game, then that's GREAT for you. I think this would be a very hard position to hold. Don't let material fool you! The queen may not be worth as much as the other pieces because of what it is doing. For further information, try watching some of Melikset Khachiyan's lectures on the subject.

In Game #2, however, black has a much more clear cut way to win. In my opinion, the simplest is 28. d3! followed by 29. h4 If white continues with Nh4, then 29. Re2 should be sufficient to win. Also, just because he "blockaded" your pawn doesn't make it useless. It's a passed pawn, for heaven's sake! It's got to be worth something! Here are some of it's benefits.

A) Space - To start, it controls the squares c2 and e2. However, that's not all! Once you put your pieces on those squares, you will be controlling even more space.

B) Support - This pawn is STRONG. White will need to sacrifice a piece to get rid of it. The a4-bishop is a strong helper in this case. It would be wise to keep it along that diagonal (a4-d1).

C) Tension, to guard this pawn, white's pieces are going to be tied down to the extreme. Assuming the knight comes to d2, you might consider an exchange sacrifice to get rid of the best defender. From there, it should go pretty well because you can deal with other matters (h5-h4) while white tries to stop your pawn.

Conclusion: 28. d3! is an excellent move. I expect in the actual game, you may have run into trouble concerning the continuations, or perhaps I am missing some miraculous response. Nevertheless, it certainly offers some advantages.

Computer Analysis: In Game #1, white is actually winning by a reasonable margin. However, like I said, black has the stronger attack. Here is the continuation suggested by Critter and Stockfish.

In Game #2, the computer does suggest 28. dxc4, but only by a slight margin. Also, it only makes since to play this line if you can calculate it to the end. Here is the "best" continuation according to Critter and Stockfish.

Again, you must consider the difference between the move that you have the ability to play and the move that the computer suggests. In the same way, a tactically inept player would never logically play the Najdorf Poisoned Pawn variation, and an endgame failure would be well-advised to keep some pieces on the board. Play what you can, and play what gives you practical chances.

I hope all this has helped! I know it has been long-winded with quite a bit of amateur analysis, but there are bits of wisdom from Khachiyan thrown in with the rest of it. If you have any questions about my analysis, feel free to contact me!

For the second game what move did your opponent play after you played 28...d3?

For the first game h3 is best toaliminate Black's threat of the back rank mate. 

I will post the continuation variations with my next post. 

Thank you for your post, it was excellent!  I agree with you in that most human players would not see 28... dxc3 - great variation though, especially 31... Rd1!. The key issue with the second game was that I made critical mistakes early on and allowed black to free his position with exchanges.  If I had continued by maintaining the pieces and attacking with your suggested ... h4!, I should have won that game.  Also, just for fun, here's how the games continued: