This page gives a list of recipes for the most common operations for working with the PSI (Program Structure Interface). Unlike Developing Custom Language Plugins, it talks about working with the PSI of existing languages (such as Java).

How do I find a file if I know its name but don't know the path?

FilenameIndex.getFilesByName()

How do I find where a particular PSI element is used?

ReferencesSearch.search()

How do I rename a PSI element?

RefactoringFactory.createRename()

How can I cause the PSI for a virtual file to be rebuilt?

FileContentUtil.reparseFiles()

Java Specific

How do I find all inheritors of a class?

ClassInheritorsSearch.search()

How do I find a class by qualified name?

JavaPsiFacade.findClass()

How do I find a class by short name?

PsiShortNamesCache.getInstance().getClassesByName()

How do I find a superclass of a Java class?

PsiClass.getSuperClass()

How do I get a reference to the containing package of a Java class?

PsiJavaFile javaFile = (PsiJavaFile) psiClass.getContaningFile();
PsiPackage pkg = JavaPsiFacade.getInstance(project).findPackage(javaFile.getPackageName());

How do I find the methods overriding a specific method?

OverridingMethodsSearch.search()