My base currency is the Singapore dollar (SGD), and I want to speculate on the USD/EUR exchange rate. Suppose I believe that that the US dollar will soon strengthen against the Euro (i.e. each USD will be able to buy more EUR). What instruments do I buy to profit in terms of SGD if my guess turns out to be correct?
You could try margin or futures trading. There, you short EUR/SGD (borrow EUR and sell it on margin or open a short position on futures) and long USD/SGD with the money you get from shorting EUR/SGD.
Assuming USD strengthens against EUR and SGD weakens, your long position profits would be more than your short position losses. On the other hand, if SGD strengthens, your short position profits would be more than your long position losses.
Alternatively, you could just long USD/EUR or short EUR/USD and convert your USD or EUR profits to SGD at the end.