I've just overhauled my carbs, so while it's fresh in my memory I recommend:
If the bike is running, spray some brake cleaner at the throttle shaft on the engine side, if there's no increase in revs you can save some time and not bother dissembling the throttle shaft as I found those o-rings were still in top shape (replaced anyway while I was there) and I've read a couple of times that these o-rings last a long time.
Still check that the butterfly valve is on the correct way though, see this link by Snowbum which has photos of how it should be (and it's good to read through before you start) -
http://bmwmotorcycletech.info/bingcv.htmTry and loosen the two carb top screws and four choke body screws on each carb first before the final order of parts - you may have a seized screw that is or ends up unusable again.
The five (each side) o-rings are: largest on the venturi, second largest on the throttle shaft, third largest on the choke shaft and the two smallest o rings are for the idle jet and idle mix screw.
I think you've got the Clymer manual - use that to find the order of doing things, it's pretty clear.
You can expect to take at least a day to take the carbs off, pull them apart (I recommend doing one at a time so you don't mix up parts), clean everything, put them back together and put them back on the bike.
Have a couple of cooling beverages after cleaning the parts, this is the most time consuming part. Assembling the carbs is pretty straightforward and by far the most fun part!