import javax.xml.transform.Templates;
import javax.xml.transform.Transformer;
import javax.xml.transform.TransformerFactory;
import javax.xml.transform.stream.StreamResult;
import javax.xml.transform.stream.StreamSource;
import javax.xml.transform.TransformerConfigurationException;
import javax.xml.transform.TransformerException;

...

// The XSL source:
StreamSource xsl = new StreamSource(...);

// Create the transformer:
TransformerFactory factory = TransformerFactory.newInstance();
Templates template = factory.newTemplates(xsl); // can throw TransformerConfigurationException (parent exception is: TransformerException)
Transformer transformer = template.newTransformer(); // can throw TransformerConfigurationException

// The data XML source
StreamSource data = new StreamSource(...);

// The transformed output:
StreamResult out = new StreamResult(...);

// Transform using the Transformer instance:
transformer.transform(data, out); // can throw TransformerException

Have a look at the StreamSource API and StreamResult API to understand the various ways by which it can be instantiated.