The beach is about a 15-25 minute walk depending on which route you take and how fast you walk. You take the same route(s) to get to the nightlife.
Go left as you leave the apartments and you have two choices:
At the large roundabout on the main road you can go straight across and follow the main road until you reach another roundabout.You go left and then cross the main road to get to the path/promenade which runs along the top of the beach. This is the longer of the two routes.
Or you can turn left at the first large roundabout and walk down past the Plaza Real apartments until you reach some waste ground. There's a dust track which crosses the waste ground. It leads to a small path between two smallholdings which then leds to a road through a small residential area. Follow this road down to the main road. Cross this and walk straight ahead, up a slight hill until you reach the promenade. This is shorter but is probably only advisable during the day. A taxi home at night is only a few euros.
Bear in mind it was 2008 when I stayed there (at the aforementioned Plaza Real) so the waste ground route may well not be there if it's since been built on.
Ask at the reception, they'll tell you - it's how we found out about the shortcut..