How do the clients in a WLAN communicate with the AP (Access Point) based on IP in the Network Layer?
The Access Point operates transparently at Layer 2, thus any Layer 3 protocol (IP, IPX, Appletalk, etc) can be run across the device.
If you think of the device like a standard Ethernet switch or hub the concept is fundamentally the same except that one interface is an 802.3 Ethernet Interface whilst the other is an 802.11 Wireless Interface. As a packet is passed from the Ethernet interface to the Wireless Interface the Access Point removes the Layer 2 information, replacing it with the correct frame structure as required for the particular 802.11 protocol.
It is useful to think of the 802.11 frame (Layer 2) as almost identical to the 802.3 frame in that it uses MAC addresses to identify which host is sending and receiving any particular frame and as such the IP address, subnet, gateway, etc are not relevant to the access point.