After they establish some lovely correspondence with you, fall in love and maybe even send a couple of cheap presents, they will either:
a) be almost on their way to meet you, but something will happen to them: they will get robbed, beaten, get into the hospital, or other misfortune will happen and of course you will be their only contact to ask for financial help, or:
b) tell you that their employer pays them with Money Orders or checks, and they can't cash them in Nigeria. They will send you the Money Orders or checks and ask you to deposit them into your bank account and then wire the money to them via Western Union. Usually they say to keep some money for your trouble. Needless to say, those Money Orders or checks are no good, and not even worth the paper they're printed on. If you cash them or deposit them into your account, Money Orders or checks will come back after few weeks as fraudulent and you will be responsible for paying back the money to the bank and sometimes even charged for passing counterfeit instrument.
There is also a re-shipping scam, when they will ask you to re-ship goods for them. These goods are purchased with stolen credit cards. Never re-ship anything for strangers, especially to Africa. There is a reason why online merchants usually don't ship there.
There are also military scams (for God Sake, there are NO American Generals browsing dating sites and NO military man will EVER ask you for money.
Then there is a recovery scam - a scammer recontacting you pretending to be FBI, EFCC or any other authority, telling he can help you recover your money... but for a fee, of course.
And finaly there is a "stuck parcel" scam, when they supposedly sent you goods/gifts, but they got stuck somewhere on the way (for example, on the customs) and you have to pay to "customs" or some bogus shipping company to get them.
All types of scams are described in details on Romancescam