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Most wireless routers have an option called "attached devices" or similar, this will allow you to see all wireless clients hooked up to your router, whether physical (ethernet) or wireless (802.11). But this depends on the router that you have.
With a little more information about it I'm sure we'll be able to help you know if you have that option or not, and how to navigate to it.
Should configure it with WPA2-AES encryption using a reasonably strong key. That way only devices you've given the key to can connect, but it gives no protection at all against people physically plugging something into your network.
Most routers will show you all connected devices, and you can sometimes use Wireshark or other sniffing tools to look for ARP or multicast packets belonging to machines that aren't yours.