Ok, I'm going to try and give it a go at explaining this, tho bear with me I haven't been taught it either and this is just what I've managed to glean, so it may be a bit off-track.
What makes the balance of payments balance is the ability of the exchange rate to shift so as to balance the 2 sides of the account out. I keep making little pictures in the air trying to explain this now, so i really need a diagram for you - but please excuse my wonky english as i point to imaginary things on my computer screen.
The factors recorded on the BOP are really the movement of currency into and out of australia, i.e they are the determinants of the supply and demand of the dollar and hence the prevailing exchange rate. So if we have a trade deficit of $10million, it means that an additional $10mill of $A is being supplied to the market than what is being demanded. With no influx of investment, the currency would depreciate to the extent such that the value of our imports actually equals the value we pay for them...our exports (ignoring investment etc for the moment), since logic says they must equal. IF I sell you an apple for $1, that apple is worth $1. If you give me US50c for that and i accept it then i believe that apple, $1 and US50c to be equal in worth, then the exchange rate is $A1 for US50c. If I sell you 2 apples and you give me that same 50c, then the exchange rate must now be $1A for US25c....
The alternative is that Australia can attract overseas investment. What this does is create additional demand for the dollar. But really, for any exchange rate/sale to actually take place, supply and demand must be equal. So now we have the same supply of dollars (i.e our level of imports, just to keep it simple for the moment) but there is increased demand for our dollar so the exchange rate rises.
Whenever any factor of supply or demand changes, the exchange rate, obviously changes so as to keep them the same. Think of the balance of payments being alternately the supply and demand of the dollar - they must equal!
Now prior to 1983, the dollar did not float, so there was not this automatic equalisation of supply and demand. It is quite possible that we may have $10million more imports than exports, but rather than our dollar falling in value so as to accommodate this, the level of money in our economy as a whole declined. It may be as though someone literally picked up a bank vault and carried it over to america. (which is why monetary policy was so much more limited - the money supply was influenced by the balance of payments, not only by open market operations).
Just think of it as a scale i suppose.
I dont think i'm explaining this very well, and I'm really sorry if this confuses you. its not meant to. Just accept that it will balance because demand of the australian dollar must equal supply.