The pulse can be taken in different places where the arteries are accessible: at the wrist (ulna and radial pulse), neck (carotid pulse), or ankle (posterior tibial pulse, etc.).
To take a pulse, the tips of the fingers (but not the thumb, which has its own artery), are pressed on the arteries in these places.
Taking the carotid pulse. © Rama, Wikimédia CC by-sa 3.0