There may be a few servers available to you, depending on your particular affiliation with the department and CSE research groups.
Email service is provided by Google apps/gmail, managed by OEC (the Jacobs School of Engineering IT group). There is no departmental mail server itself.
Google Apps for Engineering also provides you with Drive, Docs, Sites, Calendars, Groups, etc. for creating and collaborating.
Also available to some is a central linux login/shell account server. For access to this, you need a Jacobs School ldap account. Graduate students get an ldap account by default. If you do have one, you should have received your login credentials for this account at the same time that you received your Engineering Google/gmail account. If you need but do not have one, please send a request to CSEhelp.
To use the login/shell server, slogin/ssh/sftp to login.eng.ucsd.edu and use your ldap account and password.
If you want a personal web page, you can use Google Sites within your Jacobs Google Apps account, or you can put your html files into your space on login.eng.ucsd.edu, under a public_html/ subdirectory of your home directory. Be sure all files (under public_html/) are world-readable, and all directories (under and including public_html) are world-read/executable. Once done, your page should be reachable via http://cse.ucsd.edu/~<your-account-name>
In addition, some research groups have servers of their own. Talk to other members of your research group to determine what resources are available to you and who is responsible for approving and provisioning accounts on those servers.