There are various ways that students can get involved with real astronomy projects using actual data.
If you are in a school you can work with the Institute for Research in Schools, do an EPQ.
Anyone can take part in some citizen science such as Galaxy Zoo.
There are many other ways you can get involved, and some useful links are listed below:
How to participate in astronomy projects
2MASS The Two-Micron All-Sky Survey
AstroGrid A data-grid for UK astronomy, which will form the UK contribution to a global Virtual Observatory
ASTROVIRTEL Accessing Astronomical Archives as Virtual Telescopes
BiSON Birmingham Solar Oscillations Network
BOOMERanG Balloon Observations Of Millimetric Extragalactic Radiation and Geophysics
ESO Imaging Survey The ESO Imaging Survey (EIS) project is an ongoing effort to carry out a variety of public imaging surveys in support of VLT programmes
GOODS The Great Observatories Origins Deep Survey
ING Wide Field Camera Survey An umbrella for a variety of wide-field imaging programmes
Local Group Survey A photometric survey of the resolved stellar content of nearby galaxies currently forming stars
NEAT Near-Earth Asteroid Tracking
OGLE Optical Gravitational Lensing Experiment
UKIDSS The UKIRT Infrared Deep Sky Survey