I find that using my primary hand (my writing hand) is better than the other one.
Keep eyes on the road, you should not have to look to find your bottle.
I use my teeth to open the sippy valve, breathe in and then take a small drink and hold it for a sec before swallowing.
Sometimes I hold the bottle over the bars for 5-10 seconds to let the first mouthful have an effect, and then take a second drink.
When done I use my chest or my index finger to close the valve, and then put the bottle back in an empty cage (yes once I tried to push a bottle in where the other already was)
You should be able to put the bottle down into the cage without looking, although sometimes I take a quick glance if it doesn't go straight in.
Drinking on a climb is okay as long as its not too steep.
Straight and consistent is best.
If you're riding in a group, don't drink on the front cos
you'll slow down and that will cause the whole bunch to loose momentum.
Wait till you rotate off the front before drinking.
Right at the back is ideal.
Never drink on a downhill or anywhere the road surface is a bit sketchy.
With a bottle in hand your control is lower, and gravel or sudden potholes need a lot of attention.
Improve by practising - same as most things in cycling.
Quiet ride make sure there are no cars around and nothing coming up that may be an obstacle, and have a sip.
Don't guzzle water, it will be bad for your guts and there's a chance of some going down into the lungs by mistake, inducing a cough.
I find that I often phlegm-up within 5 minutes of a big drink, so drink less but more often.
bicycles.stackexchange.com/users/19705/Criggie
Remove bottle from bottle cage and keep riding using the hand not holding the bottle Pull up the cap with teeth Squeeze bottle in the mouth (if soft bottle) or suck liquid in (if hard bottle) Swallow and repeat if necessary Push back bottle cap with mouth/teeth Place bottle back in bottle cage
Any problem with the above sequence is either due to: lack of skills with riding one hand ==
> practice it more lack of breath during mouth filling/swallowing ==
> take shorter shots, delay drink lack of skills with handling bottle (take, open, close, place back) ==
> practice it more
bicycles.stackexchange.com/users/30865/L.Dutch - Reinstate Monica
I switched to CamelBak's podium bottle, which has a lock and a self-sealing "Jet Valve" that only has water come out if you squeeze really hard.
This has made the whole process easier (and better for your teeth)!
Also, if you keep one hand on a handlebar, and use your sense of touch with the other hand, you never have to take your eyes off the road!
My process is similar: Unlock the water bottle before you start your ride Use one hand to feel for the bottle and remove the bottle from the cage Place bottle end into your mouth, squeeze the bottle, and the water comes out!
Feel for the cage with the bottom of the bottle and place back into the cage
bicycles.stackexchange.com/users/35464/brascoball
I originally used to prefer to drink with my right (primary) hand but now prefer to use the left, with the right controlling steering and covering the brake (the front brake on my case as I'm in the UK.
Because I only drink water while actually riding, I always drink from the bottle in the downtube cage.
This is always a squeezy bottle.
This is much exist to get out than any other cage I've got.
I swap bottles or decant from a hard bottle when I'm stopped anyway, so that this is always the case.
A smooth flat road with good visibility is the best spot for a drink; the slightest of downhills works well too (less than 1%, so just sitting up
straight stops you from accelerating).
Easiest is freewheeling while getting the bottle in and out, so get a reasonable speed up before taking out the bottle,and put on a few pedal stripes before putting it away.
Glance down at the cage to get your bearings only at a sensible time.
This can be less distracting than fumbling to put a bottle away by feel, but it really does have to be a glance.
A few mouthfuls at a time is a good guide for me, and a drink before eating something, then another after is essential.
Also a drink after a gel
bicycles.stackexchange.com/users/7309/Chris H
Also have your water bottle positioned tilted up to the side of your face.
So you're sipping from the side of your mouth.
You won't have to bend your head back as far, as apposed to sipping from the front.
Chris Froome gave me the idea when I watched the Tour de France
bicycles.stackexchange.com/users/27305/Martin 
Adding to others answers If you are working and breathing hard, swallowing a mouthful of liquid without choking can be a challenge.
Take small mouthfuls to avoid choking.
If you do get more liquid in your mouth than you can cope with, tip your head forward
so the liquid runs to the front of your mouth, you will then be able to swallow it in parts.
Also, if something unexpected happens and you need both hands on the bars or brakes quickly, just drop or toss the bottle (but be careful of you are riding in a group, obviously).
bicycles.stackexchange.com/users/24228/Argenti Apparatus
Start with practising the act itself on a stationary bike and get used to the position of the bottle without having to look for it.
Then move on to a moving bike and repeat the action, take care to not have people around you while you work on your stability.
Eventually you'll be able to drink while cycling without thinking about the act itself.
I find it easier to drink from the side rather than straight to the front.
This makes it easier to keep you eyes on the road.
You should have smaller sips more often than large gulps more seldom.
This makes it easier to drink while breathing heavily and maintain oxygen intake.
You could mount the bike on a roller to practise before going out on the road.
bicycles.stackexchange.com/users/27234/Kristian Kalvå
How do you drink while riding?  What would you tell a new rider who is having difficulty getting a drink without stopping or slowing a lot?  Assume the bike has bottle cages in the usual places, and we're not talking about hydration bladder backpacks.  Question is purely about getting liquid into the mouth, not what should be in the bottle.  Inspired by this comment   https://imgur.com/gallery/o95PAOs/comment/1167254453
How to take a drink while riding?
bicycles.stackexchange.com
<hydration><new-rider>
bicycles.stackexchange.com/questions/50940
bicycles.stackexchange.com/users/19705/Criggie
Cyclists should not drink on downhill sections or sketchy surfaces. A smooth flat road with good visibility is the best spot for a drink. They should make sure there are no cars around and no obstacles. It is useful to practice getting hold of the bottle on a staionary bike without having to look at it.  It is important to drink small sips to avoid choking, drink a sip before eating and another after. If something unexpected happens, throw the bottle and get both hands on the handlebar. Practise removing and replacing the bottle in advance, and only drink when the road is clear with good visibility and no obstacles. Keep your eyes on the road rather than looking for your bottle. To prevent choking and losing sight of the road, take small sips from the side of your mouth rather than larger gulps. Drink little and often.
Practise removing and replacing the bottle in advance, and only drink when the road is clear with good visibility and no obstacles. Keep your eyes on the road rather than looking for your bottle. To prevent choking and losing sight of the road, take small sips from the side of your mouth rather than larger gulps. Drink little and often.