Does it affect all web sites?

Yes

I have no idea how I am meant to comply or to be honest what cookies are set

That isn't going to help, knowing what is happening on your website is your responsibility (as it should be). As an incidental point, if you don't know what the files on your site do, how would you know if the site had been hacked. More dangerous than most privacy issues.

Cookies for collecting user stats will need to meet the new requirements.

Beyond the above rather bland statements of legal intent, you might find this useful:

ICO on cookies

As to exactly how the law will be applied and enforced, do let everyone know if you find out, including the Information Commissioner:)

Seriously, this is a developing situation and in reality, doubt the law will be enforced well, or in great depth for some while, if at all. That is still no reason not to comply, using phones whilst driving, or wearing seat belts aren't particularly enforced either but people still get fined every day.

If you want an opinion, enforcement is only likely to be for real breaches of privacy and only when consent via browser options is widespread, some while away.

Still no reason not to get to grips with what your site is doing. A few odd results in the courts, or a malicious complaint could leave you exposed, why risk that. For many small sites, amendments to gain user consent aren't a great issue, could even be used as a visitor experience positive. No more than a remember me, or similar button people choose to tick, possibly with a touch more wording.