Both support and junger sweeping have the same objective: intelligence manipulation. The difference is that you won't have the same opportunities to use them. In the following answer, I will talk from the support perspective, which I main (but since the meta seems to be in sightstone junglers this could help anyway).
Your red trinket, pink and green wards are your best weapons. Intelligence of what you are doing is valuable to the enemy, intelligence of what your enemy is doing is valuable to you.
This is why I always itemise yellow trinket + 1 green at start. Then give priority to sightstone, preferably having it at first back is better. If you can sightstone, get it, switch to red trinket and get as many pink wards as you can afford/store with the rest of the money.
The use of pinks and red trinket are basically the same, except that trinket is free to use whereas pinks are not and trinket denies vision instantly for the duration of the sweep.
When to deny vision
In lane, when you know your jungle is about to come, you need to clear/check his path if you can. If you know tri-bush is warded, that will denied the gank 9 times out of 10.
When you see the opposing support ward somewhere and you have the opportunity to sweep without danger, you should do it. Especially if you are able to deny the enemy duo to ward the same place again.
Try to put priority to denying vision in your camp first, before getting rid of their defensive wards. It's important that the enemy gets his intel as late as possible, so unless their is a plan for the jungler to come from an unusual way, sweep from your base to the enemy's, not the other way.
When starting to roam, you want to deny the enemy the information of your movements. There are common spot for warding (see How do I ward properly in League of Legends? a bit outdated now, but has still interesting info on warding, there are some better spots now and I should update that guide). Prioritise these spots. Sweep first, then ward up, then attack the ward. The duration of the sweep should allow you to do this and this order will deny them the knowledge of what you did (did he ward, did he not?). There is an exception to the rule, if you know there is enemy nearby, ward first to avoid getting killed.
Late game (and teamfights)
The mid game advises are still in effect while you are moving around, but you can swipe more often and have an upgraded trinket.
With the upgraded trinket, try to :
- Cover multiple warding spot at once with the trinket if possible (multiple bushes)
- Try to sweep behind you when it's safe, if you do not catch a ward, continue sweeping the other spots with oracle vision (cover more ground).
When team-fights break, you will want to get intelligence on where the enemy is. Ward the place they are trying to hide in or even are going to hide in. Sweep when they try to get vision of your spots or lane. Be aware that removing the ward is not always necessary, sometimes you can get advantage of the disabling effect to set up your fight and surprise them. That is also useful when trying to get map objectives like dragon or baron (not matter how many wards they have, they are blind).
Team-fights are where pink ward vs trinket is critical. Use the pinks when you want durable control of the field and trinket for local/free/quick removals. Defend your pink when possible and don't forget you might need one for that invisible jungle/adc when you will fight (You can't imagine the number of Akali that go "Huh what ?" when you drop a pink in their shroud for an instagib).
- Sweeper is free! Use it as much as possible.
- Sightstone wards are free, ward the intel spots, ward when in doubt, ward when you chase enemy into bushes.
- Never leave base without wards. If you can't have sightstone, you should not have sweeper (unless the enemy support is highly vision dependent), so stay on green trinket and get at least 1 green ward.
- Keep your pinks stocked at two whenever possible (defaults to 'always' when enemy has a stealth champion)
- Upgrade sweeper when you get you core items (sightstone + boots + maxed support item), don't go for something else unless you have a strong reason to.