My brother i feel you, i had asked the same question a lot of times and must times the only answers i get are very big headaches, but over time i kindda understood a few things about the naija recruitment terrain, first as the days go by the number of unemployed "qualified" graduates increase, and if you check the number of people required for particular jobs then you might see that ur chances are in the scope of 1 to 1,000,000 or at best 10,000 people, all of them with the same if not better qualification than you.
Then we consider the fact that people within HR or even the consulting firm in charge of recruitment have their own "candidates" then you beginning to see and almost impossible task of scaling even the CV check, cos some recruiters will not get to your qualification before they toss your CV into the trash.
So i have this little piece of advice for you and anyone who feels the same way, develop yourself in anyway you can, attend seminars, workshops and register for programmes you know can give you an edge, if you're financially capable get a post degree certificate, be it your masters or a post graduate diploma.
But most especially and i think that's the problem these days, try and start something, do something with your time no matter how small the money is, be it teaching , private coaching, or even a sales girl or guy for one small shop or a one man company, these odd jobs as they are do not pay much infact they pay next to nothing but they provide you with the minimum acceptable experience years must companies now ask for, but please and please again don't leave a long period of inactive on your CV that you cannot defend, cos they'll always see it as you being lazy and that definitely will not get you anywhere.
The fact that you start small doesn't mean you won't get there it only means it'll take longer and you'll come to appreciate your job better.