This is kassieren in the sense of entering something into the Kasse, so not specifically to do with cash (after all, the customer might pay be credit card). It made me go back to a till manual I translated recently, which had instructions like:
Der Artikel wurde eingescannt und steht in der oberen Zeile auf dem Bildschirm. Um den Artikel zu kassieren, betätigt man nun die Taste PREIS, so wie es im Bildschirm angezeigt wird. Nun steht der Artikel in der unteren Zeile auf dem Bildschirm.
(In other words, you can get the till to just read the item if, e.g. the customer just wants to know the price, but if the customer is actually going to pay for it, then you need to "kassieren" so that the till records it as a sale). You could call it "putting it through the till", but in the absence of a specific English word perhaps just "enter it in the till" will do the job.

--------------------------------------------------
Note added at 21 mins (2006-02-10 20:41:18 GMT)
--------------------------------------------------

"by credit card" of course