Veteran DM here.
1) Intimate knowledge of the rules and the campaign makes improv DMing easier.
2) What is your role in the game? Different DMs have different answers. My role was to ensure the players had fun.
3) How is the story going to progress and who makes the story? DMs vary in how much control over the plot they give the players. I run a sandbox campaign (meaning the players are responsible for actively creating plot) however this does not fit every group. Just avoid going too far to either extreme.
4) DMs rarely control player characters. Mind Control is better operated with player cooperation. When a player is gone, I let the party act as if the character's unique utility abilities are there (say healing or teleportation) but the rest of the character is ignored.
5) It is usually a very bad idea for the DM to have a player character. (Google DM PC) However it is your task to control NPCs like hirelings.
6) A DM screen is not needed if you are doing improv. Your campaign notes should be short enough to memorize, the charts are in the books and you can hide rolls that need to be hid with your hand. (Very few rolls need be hidden. Opposed checks like stealth are one example)
7) I am cheap. I use a GO set as a board, walls and generic enemies. Additional enemies and PCs are represented with unique dice. (Barbarian is the d12, Wizard is the d4 ...). A dice roller is an acceptable alternative for die rolls.
8m) Try to say "yes". Sometimes you might have to say "yes, but".
Ex:
Can I swing from the chandelier into battle as part of my charge? Yes.
Can I use a ladder to pin my opponent? Yes, make a check.
Can I use the ice to increase my movement speed? Yes, but you might fall prone.
9) Circumstance modifiers are your friend. Reward players when they act intimidating as part of roleplaying the intimidate skill check. Reward them for innovative thinking like throwing gravel onto a patch of ice.
Any more questions?
Here is a good forum to browse for more information, ideas, advise, homebrewed stuff ...