replace background with transparency after selecting with magic wand

Several ways, but all require that you're not working on a background layer. Click on the lock icon on the background layer in the layer panel to change it to a normal layer.

1. Press the delete key to erase the area selected - this is not the best option.

2. Hold the alt/opt key and click on the layer mask icon at the bottom of the layer panel. This is a better way to do it, as it's non destructive. You can then edit the mask by painting with black or white.