Hi, the previous poster is correct. Tickets usually sell out a month in advance.
You can buy your tickets 3 months in advance on the Alhambra website. https://compratickets.alhambra-patronato.es/
If you already have tickets, enter through the Puerta de la Justicia. If you need to wait in line to print/pick up tickets you will need to go to the main gate, and there may be a line so plan ahead for that.
You can walk up to the Alhambra via several routes. The easiest is probably via Cuesta de Gomerez. Of course you can also take a taxi, but the bus is a simple option. Hop on bus C3 and get off at Puerta de la Justicia. You can walk back down or take the bus again. You can find the bus map here: http://www.lovegranada.com/transport/granada-bus-map/
Any hotel in Granada will be convenient for getting to the Alhambra but it is at the top of the hill. You can stay nearby but then you will be away from most of the bars, restaurants and other sights of Granada. There are even two hotels within the Alhambra complex. But I would stay in the lower Albaicin, perhaps close to the river. Or in the Realejo or the area near the Cathedral.