In this article, the problem of training federated learning (FL) algorithms over a realistic wireless network is studied. In the considered model, wireless users execute an FL algorithm while training their local FL models using their own data and transmitting the trained local FL models to a base station (BS) that generates a global FL model and sends the model back to the users. Since all training parameters are transmitted over wireless links, the quality of training is affected by wireless factors such as packet errors and the availability of wireless resources. Meanwhile, due to the limited wireless bandwidth, the BS needs to select an appropriate subset of users to execute the FL algorithm so as to build a global FL model accurately. This joint learning, wireless resource allocation, and user selection problem is formulated as an optimization problem whose goal is to minimize an FL loss function that captures the performance of the FL algorithm. To seek the solution, a closed-form expression for the expected convergence rate of the FL algorithm is first derived to quantify the impact of wireless factors on FL. Then, based on the expected convergence rate of the FL algorithm, the optimal transmit power for each user is derived, under a given user selection and uplink resource block (RB) allocation scheme. Finally, the user selection and uplink RB allocation is optimized so as to minimize the FL loss function. Simulation results show that the proposed joint federated learning and communication framework can improve the identification accuracy by up to 1.4%, 3.5% and 4.1%, respectively, compared to: 1) An optimal user selection algorithm with random resource allocation, 2) a standard FL algorithm with random user selection and resource allocation, and 3) a wireless optimization algorithm that minimizes the sum packet error rates of all users while being agnostic to the FL parameters.