How to create wireless network

I have 1 computer upstairs that needs a wireless network adapter and 1 computer downstairs that is brand new (assuming that it already has one installed) and the modem (cable), wireless router will be downstairs.

So I take the computer downstairs and connect what to what? I will have the modem, and the wireless router.

After I am done setting it up, I just plug in the wireless network adapter upstairs and it will sense it and allow me to browse the world wide web?

Also, do I need to put a password on my router so no one can drive by, and get into my information?

Really sorry,
TERRIBLE at computers,
but good at comprehending.
*I just like to, erm, get stuff right?

-ANCIENT ;0