Multi-finger robotic hand manipulation and grasping are challenging due to the high-dimensional action space and the difficulty of acquiring large-scale training data. Existing approaches largely rely on human teleoperation with wearable devices or specialized sensing equipment to capture hand-object interactions, which limits scalability. In this work, we propose VIDEOMANIP, a device-free framework that learns dexterous manipulation directly from RGB human videos. Leveraging recent advances in computer vision, VIDEOMANIP reconstructs explicit 3D robot-object trajectories from monocular videos by estimating human hand poses, object meshes, and retargets the reconstructed human motions to robotic hands for manipulation learning. To make the reconstructed robot data suitable for dexterous manipulation training, we introduce hand-object contact optimization with interaction-centric grasp modeling, as well as a demonstration synthesis strategy that generates diverse training trajectories from a single video, enabling generalizable policy learning without additional robot demonstrations. In simulation, the learned grasping model achieves a 70.25% success rate across 20 diverse objects using the Inspire Hand. In the real world, manipulation policies trained from RGB videos achieve an average 62.86% success rate across seven tasks using the LEAP Hand, outperforming retargeting-based methods by 15.87%. Project videos are available at videomanip.github.io.