Go to http://www.livejournal.com/pay/ to purchase a paid account for another user. To buy a paid account for somebody else, select "Gift for existing user" as the item you are purchasing. Add this to your order, select your payment method, and click the button to check out.
First of all, the first two sentences are totally confusing. The first one makes you think that the whole page is for buying an account totally for another user, and it's not true - it's for paying for anyhting that you can pay for on LJ. And the second one says "for somebody else" - that sounds like "for someone else than 'another user' from the first sentence".
I'd write it like this:
To purchase a paid account for another user, go to http://www.livejournal.com/pay/ and select "Gift for existing user" as the item you are purchasing.
I'd also mention that you have to give the username of the user before clicking "Add to order".