This is usually a very easy process, but not this time: that website address is wrong. It was right last year, but since then it's been changed so you have to go to www.householdresponse.com and log in to that directly, then choose your council from the list. It took me a whole extra minute to discover this.
If there's someone who lives in the house and is eligible to vote but isn't on the list, you have to fill in the paper form and send it off in the envelope they give you. You'll get a form back (either by email or post, or neither if you go to https://gov.uk/register-to-vote); fill that in once (it lasts your entire life), and you're set.
I don't know how other countries do it, but this looks fairly reasonable to me. They need to fix that dud URL, though...