you may need to learn more about the finite element method itself, I recommend you to read some books about it like "Finite Element Modeling For Stress Analysis, Robert D. Cook" or, " Practical Stress Analysis With Finite Elements"
My suggestion is to start using the software on problems similar to those you are likely to encounter. Run some simple cases and check your results against manual calculations. That will help to build your confidence. I wouldn't get too bogged down trying to understand FEA theory in much greater detail than is given in the training manuals. You don't need to understand how an aeroplane flies to travel on one. Develop an appreciation for the limitations of the software. Some of the less used areas are full of bugs. How far you want to persevere with these areas is something only you can decide.
Meshing and defining contacts has been one of the most fustrating and time consuming problems for me. Normally more of an issue where you have mixed meshes and assemblies. Learn to recognise a compatible and incompatible meshes. Learn how to force compatible meshing by splitting surfaces or faces. Learn to identify when you need to define a contact.
Defining restraints is another big and important area. Simulation has a number of different ways of doing this and it takes a while to get you head around them. For example, take a simply supported beam pinned at one end and supported on a roller at the other end. Every engineer should have encountered this problem. Try modelling that in Simulation with a solid beam. Not as easy as it might first seem but it is possible.
You need to find ways to simplify a model and reduce the time to run a study. In a recent case I was able to reduce the time to run an FEA from 2 hrs to a few minutes by simplifying the model without significantly reducing the accuracy of the model. How many dof's can your hardware handle? How can you reduce the dof's wothout sacrificing the accuracy required? What kind of contacts should you use? Non penetration contacts are very time consuming and I generally try to avoid them but in some cases they are needed. I think you get an appreciation fo these things by using the software.