Cell-free (CF) massive multiple-input multiple-output (mMIMO) systems are emerging as promising alternatives to cellular networks, especially in ultra-dense environments. However, further capacity enhancement requires the deployment of more access points (APs), which will lead to high costs and high energy consumption. To address this issue, in this paper, we explore the integration of low-power, low-cost stacked intelligent metasurfaces (SIM) into CF mMIMO systems to enhance AP capabilities. The key point is that SIM performs precoding-related matrix operations in the wave domain. As a consequence, each AP antenna only needs to transmit data streams for a single user equipment (UE), eliminating the need for complex baseband digital precoding. Then, we formulate the problem of joint AP-UE association and precoding at APs and SIMs to maximize the system sum rate. Due to the non-convexity and high complexity of the formulated problem, we propose a two-stage signal processing framework to solve it. In particular, in the first stage, we propose an AP antenna greedy association (AGA) algorithm to minimize UE interference. In the second stage, we introduce an alternating optimization (AO)-based algorithm that separates the joint power and wave-based precoding optimization problem into two distinct sub-problems: the complex quadratic transform method is used for AP antenna power control, and the projection gradient ascent (PGA) algorithm is employed to find suboptimal solutions for the SIM wave-based precoding. Finally, the numerical results validate the effectiveness of the proposed framework and assess the performance enhancement achieved by the algorithm in comparison to various benchmark schemes. The results show that, with the same number of SIM meta-atoms, the proposed algorithm improves the sum rate by approximately 275% compared to the benchmark scheme.