Each research group has a variety of resources available for the projects they work on. Sometimes research groups own one or more general purpose servers used for multiple projects. Individual research projects may have one or more servers dedicated to a single project. Research groups may rent time on servers at other locations (such as SDSC). Or, research groups may use department provided servers if their needs are basic.
When you are working on a project, it is important for you to understand the computing resources available to you. You should talk to your adviser and other members of your group to see what resources are available for your research group. If you have funds available, you can look at purchasing a server or renting time on other people's servers (SDSC, CSEHelp, Amazon, etc.).
If your research group has its own servers, you need to find the person in your research group who is responsible for setting up accounts. CSEHelp operates servers for some research groups. If CSEHelp does operate your research group's server, you still need to find the contact person in your research group who can authorize CSEHelp to provide you access to the server and approve any alterations to the server that you might desire.
If you have a defined research project, as opposed to a class assignment, one resource that is available to you is the FWGrid cluster. At this point, it's not the fastest cluster on the planet. However, many people do find it useful for their research. More information about FWGrid can be found at http://fwgrid.ucsd.edu.