The Method Configurations section of a workspace is where you organize and configure workflows that you want to run on your data. (In case you're wondering, it's called that because in FireCloud workflows are called Methods, for reasons that are largely lost to human memory.)
This is also the place from where you will launch workflows. You will do that by selecting a method and opening its configuration (in the list of configurations available for that workspace). For a method that is already configured, all you will need to do is to hit the "Launch..." button and select what data you want to run it on, as explained in this tutorial. If you are working with a blank method configuration, you can conveniently upload the method’s corresponding input’s JSON file.
So what is there to configure in order to run a workflow? Usually, two things at least: you need to set any parameters expected by the tools that are not already specified within the workflow script, and of course you need to tell the system what data to feed to the workflow. Some workflows may require additional types of input; for example you may need to select one of several possible analysis options in the case of branched workflows, or you may have the opportunity to specify runtime options like the amount of memory and disk space provided to each task.
Finally, you have the option of setting up the configuration with or without the FireCloud data model. Some users simply cannot fit their data into the data model in a way that makes sense for their genetic analysis. Or, there are users who want to test a new method in FireCloud quickly with as little set up as possible. Within the method configuration, you can turn this ability on or off. Either way, your analysis outputs will be placed in the Google bucket after execution. One advantage of running an analysis with the data model, is the ability to specify which table you want your outputs to be registered in after execution. This helps organize your outputs in a way that is meaningful to you, as you can annotate the column headers.
The method configuration is the table that lists what inputs and parameter settings the workflow expects from you, and displays which default values have been provided by the workflow author. You must enter values for required inputs, and you can enter values for optional inputs if you like (but you don't have to). The table also includes a list of the final outputs defined in the workflow. To learn more about how to configure a method, see this tutorial.
One of the key advantages to how FireCloud manages methods and their configurations is that it allows you to export your method config back to the Method Repository and share it with others. Conversely, you can import any published method config to your own workspace. That can take a lot of the guesswork out of configuring someone else's methods to run on your own data.