Transcranial direct current stimulation (tDCS) uses electrode pads placed on the head to deliver weak direct current to the brain and modulate neuronal excitability. The effects depend on the intensity and spatial distribution of the electric field. This in turn depends on the geometry and electric properties of the head tissues and electrode pads. Previous numerical studies focused on providing a reasonable level of detail of the head anatomy, often using simplified electrode models. Here, we explore via finite element method (FEM) simulations based on a high-resolution head model how detailed electrode modeling influences the calculated electric field in the brain. We take into account electrode shape, size, connector position and conductivities of different electrode materials (including saline solutions and electrode gels). These factors are systematically characterized to demonstrate their impact on the field distribution in the brain. The goals are to assess the effect of simplified electrode models; and to develop practical rules-of-thumb to achieve a stronger stimulation of the targeted brain regions underneath the electrode pads. We show that for standard rectangular electrode pads, lower saline and gel conductivities result in more homogeneous fields in the region of interest (ROI). Placing the connector at the center of the electrode pad or farthest from the second electrode substantially increases the field strength in the ROI. Our results highlight the importance of detailed electrode modeling and of having an adequate selection of electrode pads/gels in experiments. We also advise for a more detailed reporting of the electrode montages when conducting tDCS experiments, as different configurations significantly affect the results.