With 6 characters, I aim to keep the group about 1 level lower than the adventure recommends (all the way through), it seems to balance pretty well with no other changes.
Easy way: Like other people have said, keep your party a little bit lower than the intended level.
Hard way: Increase encounter CR. Usually +1, +2 in some circumstances.
I ran Jade Regent a few years ago. We had a fairly well optimized party of 5-6, and I increased the CR of most combats by 2. The party was still rarely truly overwhelmed. The only fights they had trouble with were the fight in the cold tower against the female mage. The extreme winds made it very hard for them to engage her. The other fight they had a problem with was the ninjas since they came equipped with some real serious poisons.
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All above suggestions are worthy. I typically run with 5 to 6 players. I've found that keeping character wealth slightly behind where the wealth by level table says it should be also helps.
Of course, if players are breezing through all encounters, you may want to have a look at the "DM's guide to creating challenging encounters" that was put up on the forums by a kind soul (my apologies for forgetting your name mate). I agree with the author's approach to encounter design and it does scale well with larger groups. Have a look sometime.
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I'll give you three ideas for combat encounters; I'll address non-combat encounters separately. The game I'm GMing at the moment has had 7 players up until very recently, so this is an issue I've been dealing with for quite some time. For reference, my group is level 14 with 1 mythic tier.
1) Echoing others, keep them a level lower.
Pro: very easy to implement
Con: doesn't work at level 1, players generally like gaining more levels, encounter designs will occasionally assume abilities based on your party's un-reduced level causing polarizing issues
2) Increase the CR by +1, preferably by adding minions
Pro: fairly balanced approach, adding more enemies is generally understood as good encounter design anyway
Con: more work on your end as you have to find enemies to add for every encounter
3) Use a scaling increase based on PC type
This one is complicated so I'll explain it first. First, you determine which PCs you think compose your "core" group, generally: a heavy melee, a light martial/skill character, a divine caster, and an arcane caster. Then for each of the remaining PCs you add a bonus to all enemies depending on what they are. If they are a buff caster, increase AC and hit bonuses by +2. If they are a debuff or control caster that relies on saves, increase saves by +2. If they are a damage dealer or non-save offensive caster, increase HP by +50%. These bonuses are per character after 4.
Pro: fairly balanced, accounts for your specific group's composition
Con: I've only heard of this in theory, and have never seen it used to verify effectiveness, though I frequently increase HP of enemies by as much as x5
I would recommend #2 unless you feel like trying #3. There are more unseen issues to level-lag that I'd be willing to wrangle with.
Non-combat encounters: this one is the real challenge. Ideally, you would add additional obstacles, hazards, and challenges to require the assistance of additional characters. In reality this is probably too difficult and time consuming. The quick and dirty solution is to increase all DCs by +2 to encourage aid another actions.
TL;DR- Add more monsters and increase non-combat DCs by +2.
My groups vary between 5-7 PCs. I wanted to echo the comment pointing you to the Everyman Gaming blog. The original article is in a guide here on the forums:
GM's Guide to Creating Challenging Encounters
I will use that approach on encounters that seem important. It takes a very small amount of work, but really, not that much. You simply buff the encounter by the method that Alexander suggests. If it's a CR6 encounter for instance and your party is 5th level, well then it's going to be a CR +1 encounter. You tally up the points that should be there, subtract the totals of the encounter as written in the AP and add some dudes.
On the other encounters, occasionally I'll simply run them as is and allow the party to steamroll them. Often though, I'll just add the Simple Advanced template since it's so easy to use that on the fly.
Using these two approaches, I've managed to keep the party right at the suggested levels in the AP all along. Obvsiouly, gaining levels makes the players happy. As for the fights, well, everyone seems to have fun and the modules remain deadly enough to be a challenge. I have quite a few APs going right now (I have the summer off) and here's the obits at this point:
RotR: 2 deaths, PCs are at 8th level and are in the 3rd book
Shattered Star: 2 deaths, PCs are 6th level and are in the 2nd book
Jade Regent: 1 death, PCs are at 7th level just finding book 2
It's important to get numbers up in most important encounters just to try and catch up to the player's massive action economy. Make ample use of the NPC codex (clerics and wizards in support roles can make nice challenging encounters) and pick up a copy of File the Serial Numbers Off. That's a tremendous resource for beefing up your encounters in a way that will really puzzle your players and keep them on their toes.
My groups vary between 5-7 PCs. I wanted to echo the comment pointing you to the Everyman Gaming blog. The original article is in a guide here on the forums:
I think Everyman Gaming's a bit better refined than the Google Docs, personally, but I'm obviously biased. ;-)