In Asian countries, especially Japan and Korea it's pretty rude to just sit down the money on the table. The money is usually given to the cashier with both hands holding it, or held on one hand and that arm being supported by another hand somewhere in between the wrist and elbow if the table separating the customer and cashier is too wide.
When receiving the change however, the cashier should hand the money to you with both hands and you'd receive them with both hands as well, or like I mentioned with the support the other arm thingy.
Personally, I chose to do it the way I just mentioned especially in restaurants or stores that give good service. Also, when I hand over the money, I smile at them.