Trick one: Know the combat rules VERY well.
Trick two: Teach the players to quickly determine what DCV they will hit. The describe their action, you feed them any modifers that may apply, they tell you what they'll, you tell them if they hit, they tell you where they'll hit it (if applicable) and how much damage.
Trick three: Detailed Combat Record sheets. Have all of the important numbers for the PCs and NPCs in one easy to read sheet. When a PC is attacked the only thing you should be missing is the PC's current DCV (as it may have changed based on their last action). Roll to hit, determine location and damage, subtract defense, tell the player.
Trick four: See trick one. Never look up anything in the rule book during game time. If you don't know the applicable rule, make up something fair (lean towards favoring the PC), then look it up afterwards so you don't have to do that again.
Trick five: Never discuss (argue about) the rules during game time. Right, wrong, or indifferent; the GM is right. If a player feels you've made a mistake he can discuss it with afterwards. This is real important as Hero (like any other complex rules set) tends to attract people who seem to enjoy arguing the rules.
Trick six: If playing with neophytes, I use a modifed version of the character sheet that includes EVERY key number they need and none o the ones they don't need (it has no power/skill/stat costs on it, but it has every important character combat facet spelled out in very simple terms, including modifed OCV values for each type of attack the character possess). This way, people who aren't familiar with the system don't have to hunt around the sheet or calculate anything in their head other than [Modifed OCV + 11 - 3d6 = DCV I'll hit].
Trick seven: NEVER TWEAK THE NUMBERS ON YOUR VILLAINS. Villains don't need to be cost effective, and they certainly don't need the complexity that cost effectiveness adds to a character. Hell, I don't even give "mooks" a complete write-up, all they have are combat stats.
Trick eight: Once a villains is uncounscious, unless it's integral to the plot, don't give him recoveries.
Trick nine: Similar to trick 4. If a players wants to do something that isn't explicitly covered in the rules make a quick determination on how to handle it. My simple guideline:
In general, determining the success of almost any "weird thing" that a players may his character do can be handled with either a DEX check, PRE check, INT check, or STR check modifed by the standard difficulty table. (minus 1 to 3 for standard difficulties, 4 or 5 for really hard things, more than 5 for ludicrous things). If the "weird thing" was being done in the hopes of gaining a combat advantage and easy way to handle it is to, based on circumstance, give the PC automatic initiative over the opponent, or give him plus one to OCV or DCV (ass appropriate) for every two the stat check was made by.
Trick ten: Make the players think fast. Remember, an average phase represents only a few seconds. Don't let the players dawdle or go into deep levels on contemplation every phase. Give them about 15 seconds at which point you decide that they are either continuing their previous action or holding thier phase. (Yes, this one is kind of harsh, once they're used to it, the players begin to appreciate it as it mean that THEY aren't waiitng on the other players as well.)