Yes, it switches to ticketmaster.es I think a google translate will help, or another translator extension for your browser. If you don't have that, here's what I've done step by step. I speak basic Spanish and can read a lot of the website but nuances will go over my head.
www.alhambra-tickets.es
Where it says "Alhambra General" click comprar etradas (this means buy tickets)
Calendar at the bottom - click your day. If it's too far in the future, it won't be clickable yet. If it's red, it's sold out.
Next to the calendar, click a link saying "Iniciar compra" (initiate buing or something like that - comprar is the verb "to buy" and iniciar is initiate).
Takes you to a page asking "¿Cuántas entradas quieres?" - how many tickets do you want. Select the number you need and "continuar" (obviously means continue)
Then you can click the time (you first select morning or afternoon). Morning is 8:30 - 14:00, the other choice is afternoon. Select your time frame, then it brings up the exact times. These half-hour slots are your entrance to the Nasrid Palace. You can be on the Alhambra grounds all morning or afternoon but you have to be at the gate to the Nasrid Palace in your time window.
Continuar
Then it asks if you need any reduced priced tickets. If you have children visiting with you, you can use this. Otherwise, there's the word Normal and a price of 15.40 euros
Continuar
Then it asks for your credit card. The credit card info is the same as buying anything else online. Just fill in your name, email, mobile number, card number, expiration date, and CVV ( those 3 numbers on the back of credit card used for verification), check the "I agree" box,
Continuar
I obviously can't walk you farther than this, as I'm not buying tickets. Paste anything you can't read into google translate, print your tickets, and enjoy!