Answer: Not very good. WPA, as part of the initial implementation of 802.11i,
includes a host of new features designed to patch the gaping holes in the
previous wireless encryption and authentication protocol, WEP. Wpa-psk, the less
secure version of WPA for those of us who do not have a PEAP authentication
server, relies upon a common pre-shared key ("psk" - get it??) to initialize the
communication.
Unfortunately, a clever hacker can trick your wireless basestation into
revealing the initial handshake between your basestation and wireless clients,
and then run a brute-force/dictionary attack on the handshake to recover the
pre-shared key. Even worse, the attack can be done offline at a high rate of
speed.
The upshot: While wpa-psk will keep out casual wardrivers, a determined
intruder, given enough time, can always hack into your network. If you use a
poor passphrase (like, oh, "passphrase"), a dictionary attack could render your
wpa-psk useless in 30 seconds. Your goal, then, is to use a sufficiently strong
password that would require an intruder to spend years (given today's computing
power) to brute-force your passphrase. And, frankly, if you have data that
people would spend years trying to obtain, then perhaps you should look
elsewhere for some stronger security.
In the meantime, there are websites devoted to telling you how to generate
random keys at home, as well as some sites that generate various WEP keys for
you. This page will generate a wpa-psk of whatever size you like, safely and
securely. (Plus you don't have to roll a die a couple hundred times.)
This page uses the javascript functions built into your web browser to
generate a random password for you. If you want to see the code for yourself,
find your browser's "view-source" menu item.
Importantly, using javascript, all of the computational work for key
generation takes place on your own computer. No-one but you knows what random
key you got. It is not sent across the internet and there is no way for me (or
anyone else) to record your key.
Compare a few other sites on the internet, where the actual key generation
takes place on their webserver and they transmit the key to you
(hopefully over a secure connection). If you use one of these services, your key
is only as secure as your trust for their webservers.