Downtube shifters will really get you in touch with your bike--more than with many other shifting systems, I believe that I can actually FEEL the rear derailleur moving in my hand when I use them.
Needless to say, I ride a lot of old road bikes.
You will quickly gain the control to shift either from various hand positions on your road bars.
Assuming the bike fits you, you should ultimately be able to use the shifters from nearly any position.
You will, of course, use the right hand to shift the rear derailleur and the left hand to shift the front.
I will talk mostly about shifting the rear derailleur, as it will require the most control and finesse.
Note also that these shifters each have two main parts that are pertinent here, the LEVER and the BARREL.
The lever is pretty obvious--it's the usually-flattened handle that sticks out.
The barrel is the round bit which is attached to the frame.
The cable wraps around this round bit--as you turn the shifter
, more or less cable is wrapped which is how the shifter moves the cable and thus the derailleur.
Ordinarily, when I reach down and the bike is in high gear--with the shift lever all the way forward and parallel with the downtube--I will grasp the lever by wrapping the thumb of my right hand over the end of the shift lever .
I press the side of my pointer finger against it and slowly pull back.
This motion has less control over precise gearing and is best suited for quickly downshifting before climbing.
If I am already in low gear and the shifter is out away from the downtube, I usually actually grasp the entire lever with my right hand.
In this mode, the tip of my thumb is on the barrel and my fingers are all wrapped around the shift lever.
Motion in either direction from this position can be very precise.
As I said, you can feel the derailleur move if you're cables are new and well-greased.
It's a good setup for shifters, in my opinion.
I can't say that I prefer downtube to integrated, but as far as simplicity is concerned... nothing beats it.
Except, perhaps, Sheldon Brown reaching down and putting his forefinger on the chain to move from upper to lower chainrings.
If you get a chance at the library, check out Understanding, Maintaining, and Riding the Ten-Speed Bicycle by Denise De la Rosa and Michael Kolin (Rodale Press, 1979).
This book describes shifting and using downtube shifters rather well, right down to the groovy 70's costume.
De la Rosa describes another method of hanging the thumb (I think)
off of the top tube while reaching with the same hand's fingers down to the shift lever.
This only would work on a frame smaller than mine, but it's another piece of cycling history.
I hope this helps.
It certainly took my mind off my work for a few minutes!
bicycles.stackexchange.com/users/710/DC_CARR
There's not much too it.
Reach down, move the lever until it's in the gear you want and adjust so there is no chain rattle.
You'll get the hang of it quick.
bicycles.stackexchange.com/users/683/whatsisname
Downtube shifters can be hard to get used to.
When I first used them (after having more experience with on handlebar shifters)
I would feel a bit wobbly when trying to shift.
It really just takes practice.
If they are not indexed (click into gear) then just push the lever (up or down) until the gear changes.
If there is some chain rattle, then adjust until it goes away.
After a while it will be second nature.
bicycles.stackexchange.com/users/1028/guitarthrower
I ride a Dawes Scorpion and it uses downtube shifters as well.
I learned how to shift both levers with my left hand, because I prefer to keep my dominant hand on the handlebars so to prevent wobblin' out on the road.
bicycles.stackexchange.com/users/3943/heyzahir
Spend some time on the bike, if your bike has down tube shifters I would suggest riding in a low position and get used to the balance of the bike when letting go with one hand.
It doesn't take long and you'll have no problem at all.
Simply ride only this bike for a couple of weeks
and you'll be all set.
After that go ahead and ride both.
I have two bikes as your describing and this is what I did.
Just a new habit to learn, don't over think it.
bicycles.stackexchange.com/users/13683/Terry Welsh
One thing downtube shifters will let you know right away is if your position is setup with your weight too far forward.
If you've got too much weight on your handsit will be very difficult to take one hand away without first sitting up.
If you want to make life simpler, replace the cog set on the back with a more modern Freewheel that has hyperglide cogs.
( Sunrace is reasonably good and easy to find ).
If you stick with the old stuff, you'll need to learn the art of slightly overshifting and then trimming back.
Eventually, you will learn to shift either lever with either hand, or even both at once with the same hand.
But it's simpler to start out by just using your dominate hand for both.
While it's hard at the start, try and keep your eyes on the road and learn to shift by the sounds.
Headphones and downtube shifters really don't mix very well.
bicycles.stackexchange.com/users/8445/Fred the Magic Wonder Dog
I have bought a vintage Campagnolo road bike, so the shifters are on the down tube.  I own a mountain bike and i am used to changing gears on that one, but don't know the proper technique to change on this one.  Update   I am concerned about the technique (which hand to use, how do you keep the other on the handlebar)  how do you know to shift in the correct position without an indexed shifter  other tips and tricks
How do I efficiently shift gears on a road bike with downtube shifters?
bicycles.stackexchange.com
<road-bike><shifter><technique><campagnolo><downtube-shifter>
bicycles.stackexchange.com/questions/2607
bicycles.stackexchange.com/users/125/Gabriel Solomon
To get used to tube shifters, spending time on the bike is recommended. If your bike has down tube shifters riding in in a low position and getting used to the balance of the bike when letting go with one hand is also advised. There is a good book that covers the subject: Understanding, Maintaining, and Riding the Ten-Speed Bicycle  by Denise De la Rosa and Michael Kolin (Rodale Press, 1979).  While using tube shifters is hard at the start, the advice is to try and keep your eyes on the road and learn to shift by the sounds. There are specific ways to use downtube shifters. Most characteristically, you could try placing your right hand to the rear derailleur and the left to the front end of the shift lever. That may vary, depending on the control, precision and speed required. In this context, you might want to familiarize yourself with your bicycle and experiment with riding in a low position or overshifting to find your balance. Another solution would be to pay attention to the sounds and downshift in case of any chain rattle. You could also refer to relevant publications to find more information.
There are specific ways to use downtube shifters. Most characteristically, you could try placing your right hand to the rear derailleur and the left to the front end of the shift lever. That may vary, depending on the control, precision and speed required. You could refer to relevant publications to find more information. A solution would be to pay attention to the sounds, specifically to downshift in case of any chain rattle. In this context, you should focus on the road and avoid headphones. You might want to familiarize yourself with your bicycle and experiment with riding in a low position or overshifting to find your balance.