In older books, I read about various theories about blood separation in amphibians, but newer books, such as Solomon - Biology (at least 6th Edition onward), mention:
Oxygen-rich and oxygen-poor blood are kept somewhat separate. The amphibian heart has two atria and one ventricle. A sinus venosus collects oxygen-poor blood returning from the veins and pumps it into the right atrium. Blood returning from the lungs passes directly into the left atrium. Both atria pump into the single ventricle, but oxygen-poor blood is pumped out of the ventricle before oxygen-rich blood enters it. Blood passes into an artery, the conus arteriosus, equipped with a fold that helps keep the blood separate. Much of the oxygen-poor blood is directed into the pulmonary circulation, which delivers it to the lungs and skin, where it is recharged with oxygen. The systemic circulation delivers oxygen-rich blood into arteries that conduct it to the various tissues of the body.
I would add to this my notes from when I was a biochem student (but studied Zoology), mentioning the arterial cone and a spiral valve. This is better described in Britannica:
The conus arteriosus is muscular and contains a spiral valve. Again, as in lungfishes, this has an important role in directing blood into the correct arterial arches. In the frog, Rana, venous blood is driven into the right atrium of the heart by contraction of the sinus venosus, and it flows into the left atrium from the lungs. A wave of contraction then spreads over the whole atrium and drives blood into the ventricle, where blood from the two sources tends to remain separate. Separation is maintained in the spiral valve, and the result is similar to the situation in lungfishes. Blood from the body, entering the right atrium, tends to pass to the lungs and skin for oxygenation; that from the lungs, entering the left atrium, tends to go to the head. Some mixing does occur, and this blood tends to be directed by the spiral valve into the arterial arch leading to the body.