Signed graphs have recently been found to offer advantages over unsigned graphs in a variety of tasks. However, the problem of learning graph topologies has only been considered for the unsigned case. In this paper, we propose a conceptually simple and flexible approach to signed graph learning via signed smoothness metrics. Learning the graph amounts to solving a convex optimization problem, which we show can be reduced to an efficiently solvable quadratic problem. Applications to signal reconstruction and clustering corroborate the effectiveness of the proposed method.