A few tips from out game of eight players (now seven, but still...)
1. Make sure your players know their characters and what they can do. Anything they can do to have the information they need for their actions is a good thing. My wizard has a printout of all his spells, divided by level, so I don't have to flip through X dozen books looking for the text. At the minimum, the players should list a book and page reference.
This knife cuts both ways, though; as DM you have to know what your NPC's can do. Use index cards to track a monster's important numbers (AC, hp, attack and damage) and maybe a couple of notes on any special abilities you think will be used* You can use the card to track things like the damage the creature takes, or any penalties (like if your ogre barbarian gets hit by a ray of enfeeblement for a -4 to Strength, you can just jot down "-2 attack/damage")
* Noting special abilities is important. I've seen too many DM's post here saying that their planned challenging encounter was a cake-walk for the PC's because they forgot to use a critical ability of the monster's.
2. Make anything that affects most or all of the group very visible. For initiative, we have a magnetic strip glued to a piece of plastic about the size of a yardstick. Each PC has a double-sided paper marker attached to one of those little metal binder clips, which sticks to the magnet strip. We also write in each PC's Dex score, to quickly resolve initiative ties. There's also markers for "Villain 1" through "Villain 8", an "Ally" card (for friendly NPCs), and a "Guest" card (if someone invites a friend to play). After setting this up at the beginning of combat, there's no question of initiative orders, and hopefully people can see well ahead of time when their action is coming up, and will start to prepare.
Along the same lines, for any whole-party buffs we use a lot (Inspire Courage, Haste, Bless, etc), we've made up large table-tent cards with the relevant modifiers printed in large text so everyone can see them. Although recently I've been thinking about switching to smaller cards, and printing several copies to hand to each player.
3. Get your players to help each other. Not just with the peer pressure stuff mentioned before, but by recognizing that players, just as much as characters, have their strengths and weaknesses. In our group, we have one or two people who are not good at math, or at least, not fast with it. But they choose to sit next to, and ask help from, other players who are good at math when it comes time to figuring out their attack bonus with Haste, Inspire Courage, flurry of blows, and four points of Power Attack**. Similarly, some people are better at spatial reasoning, and might appreciate some help when figuring out where to center their spell templates.***
As an extension to this, encourage the players to fight as a group, rather than as individuals. Games that utilize group tactics seem to go smoother, as there's no toes being stepped on. There's few things as frustrating as when your fighter has their attack all figured out and ready to go, with a fistful of d20's and damage dice ready to roll all at once to save time... and on the initiative before yours the wizard disintegrates your opponent. I'm not saying that the wizard should never help take down an ally's foe, but if the fighter was obviously not having much trouble handling their opponent, the wizard could have chosen a different target, or even a different spell.
One way to facilitate group cohesion is through allowing metagame talk between players in combats. Some DM's will wince at this, I know. In our game, there was little meta-talk allowed between characters at the early levels, but more as we advanced; the rationale was that as we fought together for so long, we started to develop things like code phrases and signals to let each other know what was going on, a few standard procedures that were followed in certain situations, and just an overall better feel for each other, an ability to read body language that told us things like "I'm badly wounded", "I'm about to blow something up", or "something's wrong".
** Telling you to have other players help with figuring attack bonuses may seem to contradict the advice that players should know their own character's abilities, but there's a difference between "I don't know how to do Power Attack" and "I know how to do Power Attack, but I can't add and subtract fast enough."
*** I know some people don't like having other players help with placing templates. I see it as a metagame solution to a reasonable dilemma; my wizard character will be more familiar with the use of his spells than I am, and his greater expertise can be reflected by the advice given by fellow players. Besides, in a large game where keeping things moving is important, would you rather have the player debate for 2-3 minutes on where to center the fireball without help, or have someone point and tell them "put it here"?
4. Make sure everyone understands the need for keeping things moving. There's no point in introducing all these aids and house rules if people have no idea what they're supposed to accomplish. It should also be understood that no matter what you do, D&D combat will take a long time, especially as levels and options increase. In our game, we ended up ditching the standard model of "X encounters of your CR per session", and our adventures tend to have bigger, grand-melee type final battles with little building up. The DM has had to make adjustments to his style (he can throw tougher things at us, for one, because we're coming into the final battle with more resources that 'expected') but it works for us.
One final thought. I've seen the "decide your actions in X time, or you skip your turn" advice given a couple of times here, and in other threads. If you feel this is harsh, try geting people to use Delay as a default. In other words, if they don't have an action ready on their turn, then they automatically Delay until after the next person in the initiative sequence. This gives them a little more time to think, without losing their action. The consequence of not coming up with an action is that you keep moving down the list, never getting a turn, until you do.
A few sessions back out then party of five 4th level characters decided to head over towards a large encampment of giants (hill giants for the most part). Our first encounter was 2 hill giants and 4 ogres I believe. We made it, but due to the situation we had enough time to prepare before setting off and had a strategy in mind when encountered them (as well as the subsequent hill giant, ogre and goblinbear patrols we faced later). We were a well equipped party though and I am sure that also helped in addition to us formulating a strategy for these potentially overmatched battles.
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