Synchronizing the Carburetor and Adjusting the Idle Mixture:
Synchronizing the carb is something I decided to do myself since I did not want to spend money at the dealer to have it done.  I researched it on the internet, especially the Shadow Rider Forum.  There I came across Post # 21898.1 by Rick Magalotti, whose excellent description the following is based on with minor changes.  It's a post from 2000 so unless you are a Delphi Plus member, you won't find it.  I took the liberty of reproducing some of his writing here.  It is really not that difficult and the most expensive item is the carb synchronization manometer.  I bought mine from Dennis Kirk for about $45 and the kit comes complete with all you need.  The following describes the step-by-step procedure with pictures following that.
"    Carb Synch Kit.  The kit I bought comes with a four manometer tubes mounted on a metal plate  (you only need two since you only have two carbs), clear plastic tubes, mercury, and long and short adaptors, plus instructions.
"    Magnetic Phillips Screwdriver
"    Metric Socket Set
"    7 mm drive socket and 6" extension (a regular screwdriver will work too) for adjustment of the carb adjustment screw 
"    About 4 ft (or whatever your setup requires) of clear plastic hose, 3/8" diameter, and a 3/8" hose connector to attach to the bike's fuel line.
"    I know this will be a difficult step but try to suffer thru it...LOL.  Warm up engine by going for a ride.   
"    Remove the seat and tank (make sure you are back home and the engine is off...ha ha).  Set the tank on a bench, pickup bed, anything that is higher than the bike and within a couple of feet.  You'll need to supply fuel to the bike via the 4 ft hose.
"    Connect the 4 ft clear hose from the tank outlet to the bike's fuel line using the hose connector.  Turn on gas and check for leaks.
"    Remove right and left cylinder head intake port screws.  These screws are bright silver and each has a flat washer.  Look where the black rubber intakes from each carb enter the head, where the clamps are).  Look between the cooling fins.  Use the magnetic screw driver to remove the screw.  Make sure you coax the washer onto the screw with another screwdriver or it will drop into the engine cavity (it is aluminum so won't cling to the screw).
"    Screw in the vacuum line adaptors hand tight and attach the vacuum lines to your carb gauge next. The instructions will tell you how to fill the mercury and connect the lines.  Mount the manometer high, near the bike and so you can read it when you twist the throttle.
"    To get at the adjustment screw, look down form the top where the gas tank was, between the small white plastic reservoir on the right and the black plastic air intake boot for the left carb on the left.  Rotate the throttle and you'll see the 7 mm slotted, hex head screw rotate up.  As you'll see, you can therefore use a long, regular screw driver or the 7 mm socket for the adjustment of this screw later.
"    Return throttle to idle.
"    Start the engine and run it to about 2,500-3,000 rpm.  If you don't have a tach, about a 1/4 turn of the throttle or so the mercury rises to about 24 on the scale will be close.  Watch the mercury rise in the tubes and note the difference between them.  The Honda manual says that they are ok of the difference is no more than 40 mm or 4 cm Hg.  Don't gun it too hard or you'll suck mercury into the carbs.
"    To adjust, STOP THE ENGINE.  Rotate the throttle so you can reach the screw.  To decrease the vacuum on the rear cylinder, turn the screw clockwise. Make SMALL adjustments (1/8 of a turn at most).  Snap the throttle a few times and repeat the previous step.  Adjust again if needed.
"    Finally, if you have a tach, adjust the idle speed to about 1,000 rpm with the engine running using the thumb wheel near the left carb.  If you don't, adjust until the engine is just puttering nicely at warm idle.

Carb sync manometer with hoses
Long and short adaptors.  The long ones will be the ones you need.
Left cylinder.  Location of the vacuum screw which you have to remove and replace with the long adaptor.
Right cylinder location of vacuum screw.  If you have the Cobra chrome cover, you'll need to remove it.
Location of the adjustment screw.

This is how I connect the hose from the fuel tank to the fuel intake on the bike.
Connection of the manometer hoses to the bike.
There is an idle mixture adjustment screw on each carb.  The pictures below show where they are.  From the factory they are plugged with a soft plug which you need to drill out.  There are two ways to do this.  First, use a small bit, 1/8" or so, and carefully drill a hole in the center of the plug.  Then use a small screw driver to adjust.  This way you still have the plug in there and the mixture screw cannot fall out.  Or you can remove the plug completely by screwing a sheet metal screw in the small hole and using a pair of pliers work out the plug to expose the screw.  Either way, with my setup (V+H exhaust, K+N filter and DAJ) I backed my screws out to 3-1/2 turns.  This seems to work ok.  Popping is limited to hard decels after a long, full throttle run or hard acceleration. 
Left cylinder mixture screw location.  I drilled my plug out completely.  After adjustment, I replugged the hole with a green play dooh type of stuff my kids had (read about it on the Shadow Riders Forum).  It's the sticky stuff you can stick posters to the wall with.  Works great and is still pliable after 6 month.  Just a safety precaution to stop the screw backing out but at 3-1/2 turn you probably won't have a problem.  By the way, this picture also shows the idle adjustment thumb wheel and the green hose is the fuel line for the DAJ.
This is the idle mixture screw location on the right side.