Here's what our group has found helps:
1. Dry-erase markers, a draw-upon battlemap, and minis
Its quicker and easier to calculate things when they're visible.
2. Dry-erase whiteboard upon which to track Initiative order, damage dealt to bad guys, ongoing status effects, marks, etc.
We're at the point where bad guys often get three or four status effects against them when you include marks, weakens, combat advantages, etc - plus just jotting damage down real quick, and having people be able to glance at the board to answer questions like who has taken the most damage, who is bloodied, etc .. really helps people plan their move before their turn starts. It helps that our players can see the init, and start thinking about their next move when they are 'on deck' .. as a DM, you might try using the phrase "you're up" and "you're on deck" to get people to start thinking ahead of time instead of just watching the action.
3. Printed out Character Builder sheets.
Sounds obvious, but its a big help. We keep right on using the dry-erase markers: each players has their character in a 3-ring binder. The binders have plastic sleeves into which the character-sheets go. Hit points, temporary modifiers to defenses, status effects, etc, get written on the plastic sleeves; powers get crossed off as they get used. Its a very visual way of seeing what options you have left, and its very quick to "clean up" between encounters.
4. Enemies run away.
Not every enemy needs to fight the party to the death. Really. A 'smart' BBEG is going to run when the fight has gone against him .. and it can actually be massively satisfying to beat him after facing him two or three times. Similarly, most of the rank-and-file will break if they're bloodied and the BBEG is down. In fact, I tend to set a "break and run" trigger for each monster-group when I'm writing the encounter; it means combats can be a little tougher than level-appropriate .. if the bad guys 'crumble' when a key linchpin goes down.
5. No helping. Period.
Seriously. Our veteran players do NOT bog the game down by pointing out to the newbie how she could get one more guy in her close-blast, or whatever ... they let her do her action, rather than running a five-minute conversation about the many different options which just confuse her all the more. Yeah, they all cringed when she burned an Encounter power to dust a Minion this session. She'll learn. And the party still won the fight.
(Folks do chip in the 'Oh, and +1 from our battle standard', or whatever, if they notice that somebody missed something.)
6. DM monster sheets
Print out each monster's stat block. Or have it available on PC / in the module / etc, before each combat. We've got a couple plastic "stands" which you can slip a sheet of paper or two into, so the DM have the monsters right there in front of him. Its a quick glance to spot AC, Fort, Ref, Wil, bloodied value, etc .. and he can use those dry-erase markers on the stands to cross off powers as they get used, or re-rolled.
7. Cheat sheets
Its kinda like DM's screens, but .. we handed out cheat sheets with the things you can do on your turn, which type of action is required to do which Skill check in combat, what the various status effects are ... Pretty much, every player should have these at their fingertips at any time in any battle, so there's no looking up in books, asking, etc. That goes right back to the "decide what you're doing before its your turn" concept - it only works if you know the rules, or can reasonably be expected to have found the rules before your turn came up.
. . .
Wow, when I first started typing this up, I didn't think there was much of a "trick" to it .. but I guess playing rpg's for 20+ years does give you a real repertoire of tricks; each of those mentioned really does shave a considerable chunk of time off of each encounter.