We describe how microwave spectroscopy of cold fermions in quasi-1D traps can be used to detect, manipulate, and entangle exotic nonlocal qubits associated with "Majorana" edge modes. We present different approaches to generate the p-wave superfluidity which is responsible for these topological zero-energy edge modes. We find that the edge modes have clear signatures in the microwave spectrum and that the line shape distinguishes between the degenerate states of a qubit encoded in these edge modes. Moreover, the microwaves rotate the system in its degenerate ground-state manifold. We use these rotations to implement a set of universal quantum gates, allowing the system to be used as a universal quantum computer. © 2013 American Physical Society.