The Alhambra has changed the visiting hours to make it simpler. As of April 1, there are no more morning or afternoon tickets, just all-day tickets.
The timed entry (as before) is for the Nasrid Palaces. You should plan to be at the entrance about at least 15 minutes beforehand (and allow more time if you'll need to check any large bags and backpacks). Once you are in the Palaces, you can stay as long as you want. There's a one-way path through the buildings, you can backtrack if you want, just have to exit at the other end. You can enter the campus (it's huge) any time before that. I'd recommend entering at the main entrance where you can pick up audio guides and maps and get other information. You can enter the other ticketed areas at any time during the day from opening to shortly before closing. The museum in the Charles V palace may close earlier, so check.
You can get your tickets in Spain at any Caixa ATM in Andalucia (Granada, Sevilla, Cordoba, etc). Caixa is the largest bank in Spain, so there are machines everywhere. You must use the same credit card you used to buy the tickets. Just put your card in the machine, choose English, and follow the easy instructions. It takes several minutes because the machine prints each ticket while you wait.