Are you trying to first update to 7.0.6?
If so, you can't as the signing window has closed. If you already have 7.0.6 (or any lower 7.0.x version), then you can jailbreak using Evasion7. Do NOT use the Update button in Itunes as it will try and update to 7.1 which is NOT jailbreakable at this time.
Thanks all I have always Jailbroken my phones, however I stopped when the 5 came out. I did the over the air update to 7.0.6 about 2 months ago, but have not jumped to 7.1.
Last time I JB there were a lot of dead links in Cydia, and a lot of stuff that just did not work, I am just curious how the new JB is working on iOS7.0.6