I have read the following:

http://www.acm.org/crossroads/xrds11-3/qcrypto.html

(It is an article which describes the basis for a quantum state cryptosystem)

There is one bit I don't get. After Alice and Bob compare their choice of rotational base 'b' they can discard the bits that they know will be out. After this has been done they have a binary string which can be used as a key. Apparently you can detect the presence of Eve by noticing if any of the bits in Bob's key differ from Alice's. How would this comparison be done without giving away the key?

by having part of Bob's key...

sadly Bob doesn't have a key. The article is about key exchange over a quantum medium and control signals over public medium. Someone like you could well be interested in the article - if you're not already familiar with BB84, that is!

Eve substitutes the photons she has intercepted, by encoding the bits obtained in the previous step with the bases chosen in step 4. This is known as an "intercept-resend" attack.

Simply Eve's version of a key isn't accurate which means she attempts to resend what she believes the message to contain and well it's tested as being wrong. Of course only the sender can identify the change in the message which would suggest the need for a bidirectional communication to identify not just the packet being sent but the shape of the previous packet which is probably encoded using Alice's key. (I'm not 100% familiar with the quantum Cryptology methods, since I've only read a little excerpt from Simon Singh's book "Code Book".)

I would read through it more thoroughly however I'm a bit short on time today, however you might be best trying to translate what is going on into metaphysical representation that you can 'Visualise'.

Can't say I understand your parting comment. But I shall reiterate my query using different words.

Alice sends bob a key (bit sequence) using a random encoding pattern which bob recevies and decodes with another random pattern.
Then then share coding patterns and discard bits which where not encoded using the same scheme.
They can tell if the signal was intercepted because some bits won't match (assuming Eve didn't guess the correct scheme and that the random stuff she sent out didn't match exactly)

======================

My question is how do they make this final comparison.

They can't compare over the private channel because the encoding scheme was just compared publicly. If they compare over the public channel then the key is immediately compromised?!