This situation happens when the economy of a country is not private sector driven. In solving this problem, the central government must create a business friendly environment for the private sectors to absorb the growing number of graduates from the universities yearly.
At a national level, there must be a workable employment creation scheme that would help create jobs and absorb graduates. At institutional level, the preparation of students at universities should include training in employability skills and attributes that are needed by employers.
Obed, on reflection it seems to me that we have to become entrepreneurs rather than seeking employment. Too many university graduates are currently underemployed or unemployed because we are service oriented and consider our qualifications should enable us to find highly paid jobs. But the truth is, even if we cannot get published in peer- reviewed journals we can take our chances with self-publishing books if we cannot become manufacturers.
Some measures might be improving the "presentation skills" of the students and their ability to search for a job by proper training and courses at the university. Others might include the creation by universities of proper information platforms and good relations with employers.
But the best would be if universities' curricula is regularly updated and stays in inline with demanded professions and skills by the economy. In other words the curricula should not be static but rather should be updated after regular consultations with employers' organizations and government agencies to reflect their needs.
3. Avoid mismatch. Educate people for real (not imaginary) jobs
(A disingenuous 'solution' would be to pretend a job needs a university education where in fact it does not. However, this does crowd out the jobseekers who have the right background but no university degree. From a broader society/labour market perspective therefore this cannot be called a 'solution' since it simply passes on the problem to another category of jobseekers)