This paper proposes a movable-antenna-based index modulation (MA-IM) framework that exploits the spatial mobility of a single reconfigurable antenna to create additional information-bearing dimensions for next-generation wireless systems. By discretizing the continuous movable region into a dense set of candidate sampling points and selecting representative anchors for indexing, the proposed framework converts spatial degrees of freedom into a practical modulation resource. Building on this framework, we develop a family of anchor-selection strategies with different levels of channel awareness, including geometry-based, SNR-based, max--min channel-domain, and joint constellation-aware designs. For the resulting MA-IM schemes, joint maximum-likelihood (ML) detectors are derived, along with a low-complexity two-stage detector, and unified analytical upper bounds on the average bit error probability (ABEP) are established based on the joint index--modulation constellation. The results reveal that directly indexing all sampling points is generally unreliable, highlighting the necessity of anchor optimization. The performance of MA-IM is shown to depend on key system parameters, including channel richness, spatial correlation, the number of index states, and the modulation order. In particular, increasing the number of index states and increasing the QAM order affect MA-IM in fundamentally different ways, even under the same transmission rate. Among the proposed schemes, the joint constellation-aware anchor design achieves the best error performance, demonstrating that optimizing channel-domain separation alone is insufficient and that effective MA-IM design must account for the geometry of the joint signal constellation. Simulation results further show that, with properly designed anchors, MA-IM can approach or even outperform same-spectral-efficiency QAM baselines.