How much of your user quota is in use can be found under "User -> Preferences". The disk quota for usegalaxy.org is documented in our wiki here: http://wiki.galaxyproject.org/Main#User_data_and_job_quotas.
If you are using another public Galaxy server, contact that site's support to learn about their quotas (if not published on the central default landing page - a common place for this type of information). You can also look here: https://wiki.galaxyproject.org/PublicGalaxyServers
To make room for new analysis, download to save work that is no longer needed and then permanently delete the data. This wiki and video explains how: http://wiki.galaxyproject.org/Learn/ManagingDatasets#Delete_vs_Delete_Permanently
Best, Jen, Galaxy team