- Wait until the president is playing the role of world statesman abroad. If you can help it, make sure he's gone to a gathering of his peers, such as the UN general assembly. In Africa in the 80s, the overthrown leader would likely have been military, and he would have been attending that most prestigious of khaki parades, the OAU. At such a gathering, one can assume that many of his bezzie mates would laughed at him - for getting his chair pulled from under him.
- Roll your tanks into the capital city and declare marshal law. Threatening to shoot anybody who moves an inch, oddly enough, gets you in the good books of the citizens.
- You must, must, shut down all media. If possible, play the kitsch patriotic military music, as this should remove the people's will to live, let alone stage a demonstration.
- Make sure you suspend the current constitution. After doing that, you need the coup de grace. Promise to restore democracy. The point of suspending the current rule of law is so that later, you can restore a new and improved military one.
- Even though this is not your doing, people will take to the streets. They will take pictures with tanks, celebrate with soldiers, welcome the new regime. Take credit for it, and say you're doing the will of the people.
The people will eventually get disillusioned with you. Then another military faction will take over. Repeat cycle until oil, terrorists, or communists are found in your country, at which point the US will invade.