In futures, there are no 'shares'. Traders enter into mutually enforceable contracts with each other, guaranteed by the exchange(s) and other parties. So, to 'bet' on the Peso (or indeed any currency that has a futures mkt) to go down, one simply calls one's broker and says, 'Sell 1 Sep (September) Mexican Peso at 9.18 OB'. The broker xmits the order to the exchange by one or another means, and there it sits until some other trader comes in and bids at least 9.18 for a September Peso.
This is usually called a 'short sale', in that you or I or whoever does not typically own any Pesos at the time we make the sale. You are familiar with the physical analogue of a short sale: n a store sells you a couch that you want, but can't deliver it for 3 weeks. Same deal in the couch mkt and the Peso mkt -- both we and the couch dealer either deliver the goods, ultimately, or buy back the sale.
This is exactly what we do: guarantee either to deliver Pesos to the other party on demand (after a specific date) or to repurchase our short sale. The difference in the couch market will of course be that the dealer, in the case of a buyback, will suffer endless recrimination and some amount of bad publicity (g!). The buyback option occurs in well over 98% of all trades in futures mkts.
When our order is filled, we will profit if the Peso moves lower in terms of USD, and lose if it moves higher. If, for example, Sep Peso would move down to 9.07, we might take our profit by repurchasing our short with an order like 'Buy 1 Sep Peso, 9.1050 (pronounced nine-ten-fifty) OB (or better)'. Presumably, the next bid at 9.10 or 9.1025 or 9.1050 will take us out of the mkt (however, we might well not be first in line, so it might take several such bids). At 9.1050, the bookkeeping looks like this: sold at 9.18, bought at 9.1050, gross profit 7.5 ticks x $50/tick, or $350, less whatever commission the brokerage charges us.
CME's GLOBEX is an all-electronic platform with a very good order-matching procedure (called an 'engine', for some obscure reason). Generally, bids and offers, aka 'buys' and 'sells' are matched according to time of entry and price. The algorithm is pretty simple, but was difficult to do in large quantity without sufficiently fast computers and -- more importantly, fast software. The computers became fast before the software did (historical reasons, fairly complex).
More information on the topic if you want it. I hope this has been useful to you.