How do you “OR” criteria together when using a criteria query with hibernate?

You want to use Restrictions.disjuntion(). Like so

session.createCriteria(Whatever.class)
    .add(Restrictions.disjunction()
        .add(Restrictions.eq("name", queryString))
        .add(Restrictions.eq("address", queryString))
        .add(Restrictions.eq("phoneNumber", queryString))
    );

See the Hibernate doc here.