As a GM, there are a number of ways to be prepared for combat, that will speed things up:
1) Before a session, sort out the standups, cards, and actions for all possible NPC opponents and have them ready. Preferably, in order they will be encountered.
2) Have a record sheet for opponents. The better organized it is, the better it will help. Use this to record wounds, fatigue, etc., for the various enemies. Whether it is using a pen/pencil or placing tokens on the sheet, being able to know which enemies have how many wounds left quickly is useful. Include on this, as well, a place to note/record any A/C/E pool usage (if you cannot keep that in your head).
3) Before a session, make plans for how the enemies during the various combats will act and their motivations. Of course, plans can change with PC actions, but overall enemies have a goal and will stick to it if they can. This allows you to be faster and more decisive when it comes to NPC actions.
4) Have enough dice, and try to keep the dice separated into 2-3 groups. That way each end of the table has quick access to a pool of dice. Generally, have available nearby a decent-sized pool of dice for every 2-3 people (including yourself).
5) Get the players to learn the basics for generating and reading a dice pool. It can be fun if they know how it works, so that they can generate the story/narrate the results if you are into that. If they can generate their own dice pools (excepting GM-imposed difficulty modifiers), it makes the process faster.
6) Avoid long inter-player tactics discussions during combat. Combat happens 'fast', so tactical and strategic discussions really shouldn't take place once the action starts. Charge PCs extra maneuvers (ie inflict fatigue or stress) for extra long talking during combat, if need be (but don't be too harsh).
7) Set the scene of the combat well. Quite a few slow-downs happen when players have trouble visualizing the location they are in, and the disposition of the enemies, so they have to ask questions about who is where and how far, and if they could do X, or go to Y. Good set-up/narration can avoid many such questions.