Cheapest way to ship things to Nigeria?

Three things you need to consider when sending anything to Nigeria:
1. Cost
2. Dependability.
3. Fraud and theft.
The cheapest method is through the mail or post. But this is the least dependable method and your package (particularly if it has any value) is unlikely to arrive at its destination. (Post office employees in Nigeria open people's mail and steal anything of value).
The most dependable method (but the most expensive) is via UPS, DHL or Fedex. Your package should arrive, but it will cost you dearly.
Regarding fraud: one of the previous respondents mentioned that you should never send something to someone you don't know. He is right. The risk of fraud in Nigeria is extremely high, and if you do not personally know the person you are sending a package to, you should forget about the whole thing unless you are prepared to lose whatever it is that you have sent ... These guys are extremely good at luring in unsuspecting people and will keep the scam going for a long time to try to get more out of you.

Most likely through UPS but IDK for sure.

It depends on the physical size of the item. The cheapest method is surface parcel post then Global EMS, see www.usps.com for more details.

On a side note, if you are dealng with someone in Nigera and they aren't a member of you family do NOT send anything unless it's paid for in advance and you actually have the money in your account or pocket. Nigeria is the scam capital of the world.