Non-computationally-intensive analyses can be run on your personal desktop or laptop computer. But for computationally intensive analyses (read: fMRI data), you'll need to run them to the cluster. (Not sure what a cluster is? Click here.)
We have a lab account on Dartmouth's Discovery Supercomputing Cluster. You can request an access account to the cluster here. This tutorial explains more in depth about how the Discovery works, and how to connect with it. You can find more handy tutorials on that website as well. For cluster questions, John Hudson is the go-to person.