Autocratic means absolute power in the hands of a single individual. The an Autocratic system is often synonymous with dictatorship, tyranny, or absolute monarchy. However in an autocracy, there is very little delegation in decision making. Hitler, for instance, was a dictator with absolute power. Still, he left a lot of day to day things be run by underlings. In an autocratic system, the top guy not only has all the power but has to often personally approve or direct almost every decision of government. It also means that pretty much all decisions tend to be made by the single individual which can lead to a lot overhead.
The Czar of Russia was often called an Autocrat. For example, there is an old story that in Russia there was a man who was named "Pig" by his parents. He did not enjoy the name as you might imagine. Here he could go to court and get a judge to legally change his name. In Russia, the Czar had to actually approve it. There were thousands if not millions of such little decisions that only the Czar could rule on. Hitler could care less if someone’s name was Pig or not. He’d let a judge rule on it and that was that.
A democratic leadership style is one in which the leader’s decisions are often submitted to a vote by the people or legislature. This is often confused with democratically elected leaders since there is a lot of overlap. The US President can be said to have a democratic leadership style when it comes to legislation, specially taxes. He has to submit his proposal to congress and get a vote on it. In some states, the Governor can go directly to the people with a referendum and get their yes or no.
However, there are certain powers the President has that require no approval from congress or the people. He can ask for their approval, but is not bound by it. The most undemocratic of these is the pardon power. The President’s power to pardon people for federal crimes is unlimited and can not be overruled by congress or the supreme court. He can let loose every prisoner in federal custody tonight. Congress could impeach him and remove him, but the pardon’s can not be revoked.
Another undemocratic power of the president is executive orders. These are essentially decrees by the President that have the force of law. He can make them without any democratic input. They have the force of law until congress passes a law overruling them or the supreme court strikes them down. The most famous, or infamous, instance is when President Roosevelt signed an executive order to round up and put into prison camps all Japanese Americans living in the continental United States regardless of citizenship status or if they were natural born citizens or not.
Basically, a democratic leadership style is almost impossible in the pure sense. If a leader had to stop and get a vote every time something had to be done, it would be as paralyzed as the Czar.