Mobile Edge Computing (MEC) is a modern paradigm that involves moving computing and storage resources closer to the network edge, reducing latency, and enabling innovative, delay-sensitive applications. Within MEC, computation offloading refers to the process of transferring computationally intensive tasks or processes from mobile devices to edge servers, optimizing the performance of mobile applications. Traditional numerical optimization methods for computation offloading often necessitate numerous iterations to attain optimal solutions. In this paper, we provide a tutorial on how Deep Neural Networks (DNNs) resolve the challenges of computation offloading. The article explores various applications of DNNs in computation offloading, encompassing channel estimation, caching, AR and VR applications, resource allocation, mode selection, unmanned aerial vehicles (UAVs), and vehicle management. We present a comprehensive taxonomy that categorizes these applications, and offer an overview of existing schemes, comparing their effectiveness. Additionally, we outline the open research issues that can be addressed through the application of DNNs in MEC offloading. We also highlight specific challenges related to DNN utilization in computation offloading. In conclusion, we affirm that DNNs are widely acknowledged as invaluable tools for optimizing computation offloading in MEC.