How I Can Find Cheap Flights To African cities From UK?

I am an African working in UK, I travel at least three four times to Zimbabwe and some times to some other African countries to meet my relatives. I found it very hard to book cheapest tickets whenever I travel specially in December X-Mas time and summer holidays time. Can some body guide me how i can Book cheapest flights. I also looking for some cheapest tickets to Jamaica in December can some body guide me in this regard.