Quantum simulation(1,2)-the use of one quantum system to simulate a less controllable one-may provide an understanding of the many quantum systems which cannot be modelled using classical computers. Considerable progress in control and manipulation has been achieved for various quantum systems(3-5), but one of the remaining challenges is the implementation of scalable devices. In this regard, individual ions trapped in separate tunable potential wells are promising(6-8). Here we implement the basic features of this approach and demonstrate deterministic tuning of the Coulomb interaction between two ions, independently controlling their local wells. The scheme is suitable for emulating a range of spin-spin interactions, but to characterize the performance of our set-up we select one that entangles the internal states of the two ions with a fidelity of 0.82(1) (the digit inparentheses shows the standard error of the mean). Extension of this building block to a two-dimensional network, which is possible using ion-trap microfabrication processes(9), may provide a new quantum simulator architecture with broad flexibility in designing and scaling the arrangement of ions and their mutual interactions. To perform useful quantum simulations, including those of condensed-matter phenomena such as the fractional quantum Hall effect, an array of tens of ions might be sufficient(4,10,11).