How should I connect my new WiFi Smart Switch?
There's a nice video at that link which covers things pretty well. You connect the blacks to the two blacks that connect to your current switch. 

The white from the new switch can be bundled with the cluster of white neutrals in the box, though it appears that the nut on it is already quite full. You might need to split the bundle and connect two smaller bundles with a jumper. 

The green ground wire connects to the bare ground wire bundle in the box.