The official currency in Ecuador is the US dollar. Exchanging money is relatively easy at banks or currency exchange houses ( casa de Cambios). Though this is only the case with Euros, Peruvian Soles, and Colombian nuevo soles. Other foreign currencies are difficult to exchange in Ecuador. Most non-US travelers exchange currency in their home countries before traveling to Ecuador.
There's no limit to the amount of money that can be imported or exported from Ecuador, but amounts above $10000 must be declared at customs. However, carrying more than $10000 is unsafe and unwise. It's also inconveniencing, you'll have to wait for hours as your notes are being checked for counterfeits. Failure to declare the amount you have in case you more than $10000 can also lead to your money being confiscated.
If you require more than $10000, the best option is doing a wire transfer. In most cases, it takes less than 2weeks.
While the notes being used in Ecuador are dollar bills, Ecuador centavo coins are not accepted in the US. They are identical in size and value to their US counterparts but are useless in the US. Be sure to use all your coins while still in Ecuador.
Cash is still king in Ecuador, though the banking sector has greatly improved ever since the dollarisation of the economy. Don't carry large bills. Stick with $20, 10, 5, 2, and 1 bills. Change is already a rare commodity in Ecuador and many small traders are rarely willing to give change on any amount above $10.
Payment by credit and debit cards ( especially Visa and MasterCard) is relatively common in Ecuador. This can be expensive, some businesses may charge a fee of up to 8% if you're paying by card. Most attendants will inform you of this fee before you make payment.