There is a good bus service to the Science Park from
the city centre - numberd 4 and 44. You can get on either of these from right outside the railway station. The journey time should be 10-20 minutes.
Here is a map of York bus routes.
Also, the science park website has a map.
Once you've found the science park, the building is called the Biocentre and is on the left as you go along Innovation Way. It's the building right in the centre of the picture on the left, and is also pictured on the contact page.
Travel Information page has good information on
public transport connections.