Say that you acquired an asset, a printer for an example and the price was paid in foreign currency as opposed to your functional currency. It is perfectly normal for such transactions to take place and as a matter of fact there’s nothing complicated about it.
How you would account for the transaction is as follows. Say that you acquired the printer for 100 FCU (foreign currency units) and the exchange rate was 1 FCU for 1.5 CU (currency unit, i.e. the currency your accounting is daily done in). So effectively the printer’s price is 150 CU in your books. You’d account for 150 CU to your assets and payables. Presuming you don’t have the FCU on your bank accounts (i.e. you’re not holding foreign currencies on your bank accounts alongside with your functional currencies) you shall also account for paying to your supplier 150 CU and your bank does the exchange from its resources. Note that the exchange rate applied should be from your central bank and not your local currency exchange office.
What happens however with the asset afterwards? It’s simple, as opposed to monetary (e.g. receivables, payables) balances nominated in foreign currencies, the assets are carried at the cost they initially were acquired in and their cost is not changed when currency exchange rates change.