Currency pairs are only ever expressed one way for a good reason...
i.e
EUR/USD - never USD/EUR
GBP/USD - never USD/GBP
AUD/USD - never USD/AUD
NZD/USD - never USD/NZD
USD/CAD - never CAD/USD
USD/CHF - never CHF/USD
USD/JPY - never JPY/USD
EUR/GBP - never GBP/EUR
EUR/AUD - never AUD/EUR
GBP/AUD - never AUD/GBP
AUD/CAD - never CAD/AUD
AUD/NZD - never NZD/AUD
AUD/CHF - never CHF/AUD
AUD/JPY - never JPY/AUD
EUR/JPY - never JPY/EUR
so when you say you're "short on X" or "long on Y" they know exactly which way you've traded a pair
exchange rates always expressed in the above format (1 of the currency on the left = x amount of the currency on the right) - so if you had AUD/USD rate of .9667 and you want to know what 1 USD would be worth in AUD, you divide the AUD/USD rate by 1, or 1.0344.
rule of thumb: XAU (gold) is always on the left. EUR is always on the left (except XAU/EUR), GBP is always on the left (except EUR/GBP, XAU/GBP), AUD is always on the left (except EUR/AUD, GBP/AUD, XAU/AUD), NZD is always on the left (except EUR/NZD, GBP/NZD, AUD/NZD, XAU/NZD). USD is predominately on the left (except EUR/USD, GBP/USD, AUD/USD, NZD/USD & XAU/USD) and so on. JPY is always on the
right (afaik?).
As the guys above have explained, when you buy a pair, you're selling the currency on the right of the pair and buying the currency on the left of the pair (BUY AUD/USD - hold AUD and have sold USD - you're "short on USD" or "long on AUD" in this instance), and when you sell a pair you're selling the currency on the left and buying/holding the currency on the right (SELL AUD/USD - hold USD and have sold AUD - you're "long on USD" or "short on AUD").
When you hold a currency in a pair which has a higher central bank interest rate than the other currency in the pair you're carrying trading (take rate of the currency you hold and minus the rate of the currency you sold). Placing a BUY order on AUD/USD is carrying trading (AUD = 7.25%, USD = 2%), placing a sell order on USD/CHF is also carrying trading (USD = 2%, CHF = 2.75%). So if you were short on AUD/long on USD on AUD/USD, you would effectively paying interest to your broker (whereas they pay you if you were long on AUD/short on USD in AUD/USD) with each rollover (5pm New York time each day).
HTH.