  We present an algorithm for computing zero-dimensional tropical varieties
based on triangular decomposition and Newton polygon methods. From it, we
derive algorithms for computing points on and links of higher-dimensional
tropical varieties, using intersections with affine hyperplanes to reduce the
dimension to zero. We use the algorithms to show that the tropical
Grassmannians $\mathcal G_{3,8}$ and $\mathcal G_{4,8}$ are not simplicial.
