The question of how to adjust the trigger on the Remington 700 action seems to come up on rec.guns at least several times a year. Perhaps this will help.
DISCLAIMER - changing any setting on a factory trigger is an inherently dangerous thing. The recommendations herein are an attempt to provide a safe method for performing these adjustments on this model only. If you have any doubt whatsoever about this process, take it to a gunsmith. If you are about to embark on this, make sure you know a good gunsmith who can fix it if you goof it up. Consider taking the finished job past a good gunsmith once you're done to check if the work you've performed results in a safe trigger. And make REALLY sure that the chamber is empty. The author, newsgroup moderators, and all others who may pass this information along cannot evaluate your skill level, and take no responsibility for the results of following these instructions. Also, this applies to the trigger on the factory Remington 700, using my 1968 vintage rifle as the prototype. I have no idea if it needs to be modified for the Model 7, 40-XB, XP-100, etc.
Now that that's out of the way, on to the educational part ;-)
The Remington 700 trigger group consists of the trigger, a trigger connector bar, a sear which rests upon the trigger connector bar and holds back the cocked firing pin, and a set of three adjustment screws and assorted springs and pins which hold it all together. The safety lever is attached to the trigger group, and blocks the sear motion. It does not block the firing pin, and so the safety is completely reliant on the soundness of the trigger group to properly perform it's function. An important piece of equipment you will need is a trigger pull weight scale. One can improvise by hanging known weights (e.g. a coffee can with 3lbs of sand in it) by wire from the trigger while pointing the muzzle at the sky. If using the latter, the trigger pull will be roughly equal to the lightest weight you can hang on the trigger which causes the trigger to fall.
Two screws are on the front of the trigger assembly, and one on
the rear. The top front screw is the trigger stop screw. This
controls the trigger overtravel after sear disengagement. The
bottom front screw is the trigger adjustment screw, and controls
the "pull weight", or the spring pressure holding the trigger in
position. The trigger engagement screw is on the rear of the
assembly, and controls the amount of the sear supported by the
trigger/trigger connector.
After removing the action from the stock, and identifying these
adjustment screws, try giving the mechanism a thorough cleaning
with a cleaner spray and lubricate the mechanism lightly (see
your owner's guide). Sometimes this is all that's required to
blow out leftover assembly grit, or dirt from extensive field
use, and can result in a perfectly acceptable trigger pull.
Note that the adjustment screws will likely be covered with a
locking compound and may not be immediately obvious.
If anything is not clear and apparent at this time, or at any point along the way, reconsider taking it to a gunsmith. Safety is paramount.
Okay, here we go:
Remove the trigger guard assembly, and remove the action from the stock. Cock the bolt in the receiver. The trigger pull weight is adjusted by turning the trigger adjustment screw (bottom front): clockwise increases the pull, counter-clockwise makes it lighter. It doesn't take much, try 1/8 turn to begin with and then test the pull weight. It is STRONGLY recommended that you DO NOT attempt a trigger pull of much less than 3 pounds. The stock Remington mechanism is not (in my humble opinion) intended for a target-style 2 pound (or less) pull weight. There are readily available aftermarket triggers if that is your desire. Apply a light coat of loctite, fingernail polish, or other locking compound to the screw head when done.
The overtravel of the trigger may be reduced by turning the trigger stop screw (top front of the trigger group) clockwise until the firing pin doesn't fall when you pull the trigger. Then hold the trigger back, and turn the trigger stop screw counter-clockwise until the firing pin falls. Turn about 1/16 turn further and stop. This is about the least overtravel which still maintains margin for hunting in the field. So long as this minimum is established, some may prefer more overtravel, this can be adjusted out further to personal preference. At this point, most shooters should find the trigger is quite acceptable. As before, cover the screw head with a locking compound to prevent it from moving accidentally.
Some may have a rifle which has some "creep" in the trigger before letoff. The key to this adjustment is in the trigger engagement, however, in this writer's opinion adjusting the sear engagement is best left to a gunsmith. I believe this is the most critical adjustment in terms of safety, and I don't intend to mess with it. Even Remington's earlier users guides (pre-liability-suit days) which included trigger adjustment instructions state to leave this adjustment alone. If someone out there wants to take a pass at writing for this part, be my guest (SEE BELOW). Most people (including myself) should probably only touch the bottom front screw, the Trigger Adjusting Screw.
After any messing around (including simply cleaning the trigger assembly) you should probably test as Remington recommends, by closing the bolt "smartly" at least ten times. The firing pin should not fall while doing so, but must fall every time the trigger is pulled. Another method, which requires a good recoil pad or a carpeted/padded floor, is to verify the chamber is empty, cock the bolt, then bounce the butt firmly on the floor. Either of these methods should get the firing pin/sear/trigger combo bouncing around pretty well, and test if the rifle is likely to discharge accidentally on being bounced, bumped, etc. Verify that the firing pin does not fall during any of this, including cycling the safety on & off prior to pulling the trigger.
A couple more comments:
NOTE on adjusting CREEP (from an outside source other than the author above):
The guy who wrote these instructions dismisses the consumer's ability to adjust the creep. It's just as easy and necessary as the other two adjustments.
With the rifle unloaded, of course, cocked, with the safety off, turn the back screw slowly in until the rifle fires, without your having pulled the trigger. Back off the creep screw about 1/8 turn. Recheck the pull weight.
Do all the safety checks. Additionally, rap the side of the action with a rubber hammer. If the gun fires when it's not supposed to, back the creep screw out just a little more. It's simple.