Fused deposition modeling (FDM) technology is one of the rapidly growing techniques used for producing various complicated configurations without the need for any tools or continuous human intervention. However, a low quality of surfaces results for the layered production used in FDM. It is essential to investigate a suitable method for enhancing the accuracy and quality associated with FDM parts. This study aims to investigate the impact of different parameters such as the percentage of infill density, the shell thickness, layer thickness, and the number of top/bottom layers, as well as the percentage of infill overlap on part quality and the improvement of surface finish for printed specimens achieved through post-processing. Polylactic acid (PLA) material is used in building test specimens through the FDM approach. The experiments are carried out based on the Taguchi design of experiment method using (L25) orthogonal array. Using an analysis-of-variance approach (ANOVA), it is possible to understand the significance of the FDM parameters in order to find optimal parameter combinations. The results indicate that the application of the vapour smoothing procedure (VSP) treatment enhances the surface quality of FDM components to a microstage with minimal dimensional variation. The dichloromethane chemical has been found to exhibit excellent surface finish at an infill density of 50%, a layer thickness of 0.1 mm, a shell thickness of 2.8 mm, five top/bottom layer numbers, and 0.25 infill overlap.