How to play with space?

What is the strategy involved with space and the centre? I lost both games where I clearly had a more central space which I assume is a straight forward advantage for whoever has it. 

To summarise I gained a central space plus in both games which I assume puts me at an advantage but managed to still lose. What is the correct way to play with space?

Keeping your king castled with 2 knights in front ; f3 and g3 helps a lot.. like those master games. More central attack=more cornered counterattack by opponent. So, we better keep our kings safe

Re:  move 9 in game 1, advancing wing pawns is only good in specific situations, like opposite casting.  Often if the center is closed.  Here, it is a bad move, as black plays d5 which is a good move anyway, double attacks the pawn and prevents b5.  The light square bishop can also develop with tempo which is useful in some variations.  

Re:  move 18 in game 1, b5 wins a pawn or forces the knight to the rim.  Since the whole purpose of playing rb1 was to potentially push the bpawn, gain space and timely kick the knight, it should have been on your mind.  As far as e4, it severely limits your light square bishop if you can't move the epawn -- so it should have been obvious that e5 needed to be looked at. And the fact that black gets a great square for his knight which you can never dislodge him from is also huge.  Expanding in the center can't at the cost of crippling your bishop and giving him a massive knight is a bad trade -- always have to consider piece activity.  

Instead of 9. Rb1 what is the more appropriate approach for white to progress his position? Or is that too broad of a question? Sometimes its not too obvious where I should develop my pieces such where should my bishops go in this position. Was the LSB better off being placed in d3? Not sure where my DSB should go either if I'm honest. As for move 18 b5 was something I considered but after Na5 I feared my c pawn would be weak, probably the reason I didn't play it which was stupid of me.

The classical way to exploit an advantage in space is by using alternating threats on widely separated parts of the board, in order to convert your space advantage into a time advantage... which is much easier to exploit.

Read my posts in this thread: https://www.chess.com/forum/view/general/gm-larry-evans-method-of-static-analysis

EDIT: I just took a look at your first game, and you traded way too many pieces off. If you want to exploit an advantage in space, you need to keep the board crowded.

I do sometimes play the French and Sicilian but I don't really study any theory, at my level it probably doesn't matter at all and I end up usually just playing any random classical opening or at least trying to stick with the basic concepts. If I remember correctly I don't seem to face a lot of King's Indian or French at my level for whatever reason.

Keep pieces on board, play on side with space e.g. don't trade rooks, play c5

If I were to describe the position after 3. e3 I would say white has blocked the natural diagonals for both bishops in exchange for a pawn on c4 and e3 which act as white's influence over the centre. So for white I would say for now he has limited the development of his bishops for control over the centre. For black I couldn't say much as he hasn't made many committal moves with only 1 pawn move (1. e5). That would be my attempt to describe the position, however I have no idea how accurate or rubbish my analysis is.

As for what I was trying to do, 3. e3 was simply my attempt to control the centre with the follow up d4, as for black's responses the first moves that come to mind are d5 and c5, though c5 by black may result in an isolated queens pawn which is probably a weakness for black after d4 is played anyway by white followed by a series of pawn exchanges on d4.

So the number one way to use a space advantage is to avoid exchanges. A space advantage means much more when there are a lot of pieces on the board - your opponent's pieces are cramped and they struggle to find good squares. With fewer pieces on the board, your advanced pawns can become targets and the spaces behind them weak, while your opponent isn't cramped because he doesn't have pieces to be cramped.

That's exactly what happened in game one. You have a space advantage, but because each side only has one minor piece left, the space advantage doesn't really matter. Furthermore, black's knight has that juicy d4 square, while your bishop is blocked behind his pawns - so he has the better minor piece. 

Then you trade rooks off, so, again, increasing the difference in quality between the pieces left on the board. 

Read Silman's "How to Reassess Your Chess." It'll help you understand why e5 was so awful here - surrounding the d4 square and blocking your bishop. At that point, you have to develop a plan around activating your bishop otherwise you'll just slowly lose as you did in the game. 

Game 2 is more complex, but you make some of the same mistakes. Bg3, for example, invites a trade. Black can force a trade eventually by plopping a knight on f4, but you shouldn't invite it. But the larger issue is that when you have a big center, you want to push forward and break through with it when it gives you a decisive advantage. By advancing your center the way you did, you removed it's dynamic potential - but its dynamic potential is what keeps black in check on the kingside.

So I might have played b4 rather than d5. Get things going on the queenside. But really, however, you lost here because you played the middle game poorly.  22.Nd3 is slow, and this is a position that calls for speed: 22. Rb2! threatening Rgb1 & Rxb8 is brutal. In the opposite-side castling situation, you have to play incisively and attack, especially with your king sitting on the soon-to-be-opened g-file. 

Thanks for the analysis it is much appreciated, I often still struggle to find the right moves to progress my position as seen in the diagram you showed after 11. Nd1. 11. h3 did cross my mind but I probably didn't play it as I feared one day the hole on g3 created might one day be occupied by a knight, this fear I suspect is total rubbish though. Aside from that the difference between the bishop being on g4 and h5 I don't seem to fully understand, why is h5 less active then g4? Even if it is can't the bishop relocate to a nice diagonal on g6 after h5? Also would it be correct to say gxf3 is better then Qxf3 if bxf3 since gxf3 strengthens your centre? 

As for 11. Nd5 I just simply didn't see the compensation for white's doubled pawns, if I had to guess though I would say white's compensation is in the form of greater piece activity and influence over the centre? I'm currently trying to improve my ability to find the right moves that improve my position, would you suggest studying the games of strong players and seeing how they develop their position?

You are quite right as for e4 in game 1, I would say this move probably cost me the game as after e4 his knight seems to be vastly superior to my previously wonderful bishop, I suppose b5 (as someone else here suggested) was a much better move after it forces the knight on a5 my bishop proves much better then his knight. 

In game 2 I thought d5 was a pretty decent move as in my mind it blocks in blacks bishop and forces the black knight to a7 or b8, so I thought d5 was an ok move but I'm assuming theres probably some reason as to why i'm wrong about that. As for moves like Nd3 I blame it on the fact I play like an old man and I get into some serious time trouble, Rb2 as you suggested was much better of course. I'm curious about the mention of dynamic potential of the centre, is this a concept I can read up on in Silman's book?

Correct, with whites dsb guarding the diagonal the weakness only becomes a problem if black can get his bishop onto the h2-b8 diagonal, which is not reasonably foreseeable in this position.

"I'm curious about the mention of dynamic potential of the centre, is this a concept I can read up on in Silman's book?"

Yes. There's a chapter on playing with vs playing against a big center. But looking over your games I think you'll find a lot in the book that helps you.