Bear in mind that each cylinder has 2 valves, an intake ( towards the rear of the bike, nearest the carburetor) and an exhaust (next to the exhaust outlet).
What you're looking at in this crappy little diagram is:

9 ) The valve cover
1) The valve stem
5) The tappet / pushrod
8) The tappet lock nut
7) The valve adjustment nut

It will make more sense after you take off the cover and look at the real thing.

The main thing we want to do here is adjust the (hopefully) tiny gap between the valve stem and the end of the tappet. To do this, you first remove the spark plugs & valve cover plates, then pull the starter over until the intake valve closes completely. At this point the end of the tappet will be at it's furthest point into the cylinder.
On the exhaust valve on the same cylinder loosen the lock nut on the tappet, and check the gap between the ends of the valve stem and tappet with your feeler gauge. Now turn the nut on the valve stem until you have a 0.1mm gap between the valve stem & the end of the tappet. Tighten the lock nut & turn it over again until the exhaust valve is closed and repeat the procedure for the intake.
You're going to have to do this a few times before the clearances stay there.
Clean the valve cover & the case thoroughly removing all the old gasket and any oil or grease, then use a bead of high temp silicon gasket sealant to close it back up.

Balancing K-37 Carbs

Flat twin engines are generally fitted with dual carbs, in my case these are the original K37 models.

An advantage to these is that they're pretty simple to work on. Basically you have three adjustments: the throttle cable adjustment (26) which controls the depth of the slide, a stop adjustment screw (19) that more or less "fine tunes" the slide, and a mix adjustment screw (18) that sets your air / fuel ratio.

A disadvantage to these is that spare needles and other parts are about as common as honest politicians, so anything that falls out on the highway is probably going to require a new one to be machined. And parts DO fall off if you don't keep those lock nuts tight. Also, they do require pretty regular tweaking to keep things running smooth...at least on my machine...so you'll probably develop a deep, sincere and blatantly physical relationship with these chubby beauties.

If you suspect carb problems ...generally indicated by excessive backfiring, difficulty starting even with a good spark, or having your boots soaked with gasoline... there are a few things to check before you decide to start tearing things apart. First, make sure you do have good spark and that the points and plugs are gapped properly. Next check the color of your plugs: optimally they should be a nice brown color, but in my experience that only really occurs in other peoples fantasies. Realistically they'll usually be dark, but they shouldn't be caked with carbon. Next check your floats: cut the fuel off and drain the bowls by loosening the lower filter (7), then pull your float covers and make sure that the float is seated correctly and has plenty of free travel. Check the air intake tubes for leaks and check that the nuts holding the carb body to the cylinder are tight. Make sure you have good fuel flow from the tank and that it's even on both sides.

Now determine if you're running rich or lean: this is pretty much determined by your plug colors. There are at least two screen filters that need to be checked if you're lean: in the petcock (fuel tap) under the tank there will be one at the top of the bowl and / or another inside the bowl. In the carburetor body there's another wrapped around the fuel port in the lower filter plug (7).

If those are clean and the idle / throttle adjustments are good, then the mix should be adjusted. On this model you have a fuel control mixture screw, so CCW (out) is rich and CW (in) is lean. The rule of thumb is that if the mix adjustment is on the intake side of the carb (by the air tube) it's an air control screw and therefore CW = Rich, CCW = Lean. If the mix adjustment is on the outflow side (next to the cylinder) then it's a fuel control screw and CCW = rich and CW = lean.
(Bill Glaser taught me this. Bill's a pretty smart guy, I have no idea why he rides a Ural.)

Balancing the Carbs & Setting Idle Adjustment:

Remove the breathers so that you can access the bottom of the slide. Loosen the lock nuts on the cable adjustment screws (27) and the slide stop adjustments (19), then turn out the stop adjustments until they're loose. Take a 6mm drill bit and insert it into the bottom of the breather intake then adjust the cable screw until the base of the slide is resting on the top of the bit. Now tighten down the lock nuts on the cables and turn the stop adjustments back in until they just make contact with the slide.

Assuming that your mix screws are original and the same size, (now might be a good time to check, one of mine is almost 3 mm. longer than the other) back them out about halfway and use a set of dividers to measure the thread distance from the carb body, setting them both the same. Now fire up the bike, set the spark advance lever forward, pull one plug wire and adjust your stop screw until that cylinder is running smooth. Next turn the mix screw in until the cylinder starts to choke out, then back it off slowly until everything sounds right. Plug in the other cylinder, unplug the first one and repeat the process tuning it by ear so that it matches the first cylinder as closely as possible.
Now shut it off and let the engine cool down so that you don't sear the skin off your knuckles. Again.

Block the front and hack wheels and jack up the back of the bike so that the pusher is free. Now crank it back up again and work it up to 4th gear. You need somebody to hold the throttle open now at a good RPM unless it stays in place by itself as most of the older ones do.
Now readjust your mix screws using the same procedure as before, one cylinder at a time. Do this quick so that you don't put excessive strain on the engine.

If problems persist then the likelihood is that you have a clogged port somewhere. In this case you'll need to carefully take the carbs apart and blow everything out with a compressor, then start over again.