Assistive robots have the potential to provide tremendous support for disabled and elderly people in their daily dressing activities. Recent studies on robot-assisted dressing usually simplify the setup of the initial robot configuration by manually attaching the garments on the robot end-effector and positioning them close to the user's arm. A fundamental challenge in automating such a process for robots is computing suitable grasping points on garments that facilitate robotic manipulation. In this paper, we address this problem by introducing a supervised deep neural network to locate a predefined grasping point on the garment, using depth images for their invariance to color and texture. To reduce the amount of real data required, which is costly to collect, we leverage the power of simulation to produce large amounts of labeled data. The network is jointly trained with synthetic datasets of depth images and a limited amount of real data. We introduce a robot-assisted dressing system that combines the grasping point prediction method, with a grasping and manipulation strategy which takes grasping orientation computation and robot-garment collision avoidance into account. The experimental results demonstrate that our method is capable of yielding accurate grasping point estimations. The proposed dressing system enables the Baxter robot to autonomously grasp a hospital gown hung on a rail, bring it close to the user and successfully dress the upper-body.