Generally, Napoleon was a nobody in the wider sense of the Revolution until 1796. He participated in the siege of Toulon and did help protect the Directory that was going to be attacked by a pro-Royalist rebellion with the famous "whiff of grapeshot." After this, he was promoted and given command of the Army of Italy, where he would show how to fight a modern war. Afterward, his story is famous where he would go to Egypt and then would help to overturn the Directory in order to develop the Consulship with him at the front. From here, he would basically dominate French politics by practically being involved in every aspect, ultimately culminating in the Napoleonic Code.

However, once he became Emperor and Austria decided to fight Napoleon again, he would have a very well developed logistical system which fed straight to him. Generally, everything would be done by letter, he would give an order to his chief of staff (Marshal Berthier) and it would be sent to the proper places. This would be for both matters of state and military. Such as with the standard modern state, there were different bodies of government that worked different parts so that the leadership didn't have to do it all. These ministers would be in contact with Napoleon and Napoleon had the best staff in Europe at the time, possibly ever for his time period.

As for stopping others from taking power, it was a constant threat. During the invasion of Russia in 1812, there was a rumor that Napoleon had died and thus a man named Claude Francois de Malet (who created the rumor) approached a colonel of a National Guard regiment to help him in the process of replacement of government. Documents were forged and lies spread, eventually it was suppressed by the minster of war with help of others. However, this had a negative effect on the retreat as Napoleon dashed away for France to address the coup, leaving Marshal Murat to lead the army back (he would later desert for his Kingdom and switched sides when plied by British money and diplomacy).

Generally, suppression of coups had more to do with good intelligent and loyal soldiers, which Napoleon had both in ample amounts. If there was a single thing that prevented others from taking power, it was the loyalty of the soldiers that he banked on.