When should I use a control ward instead of my usual totem ward? I don't buy control wards because they cost 75 gold and I can just use the 2 totem wards that the game already gives you, but people encourage you to buy control wards. So when should I use either one of them?
The totem ward will give your team vision, but a control ward will give your team vision and it will deny the other team vision.
Denying the other team vision is really important when setting up for objectives (Baron, Dragon) or when pressuring different lanes. If you're sitting in the top river, and the other team doesn't have it warded, the threat of giving away Baron itself can be enough to earn your team kills. Then, you can use that momentum to do Baron safely, or push down a lane knowing that you have a numbers advantage.
If you're deciding on which ward to use, you should ask yourself whether you want to deny enemy vision in an area. Control wards are so strong that you're only allowed to use one at any given time. Foregoing them entirely is a mistake, in my opinion. 75 gold is incredibly cheap to deny vision over critical areas of the map.
Good luck on The Rift!
There are a few different reasons to buy a control ward:
They reveal opposing wards and traps and disable opposing non-control wards. This can allow your team to position out of sight, which can be relevant for taking objectives like Dragon, for sieging turrets, or for ambushing the enemy in the jungle.
They do not expire. You can place a control ward in certain defensive positions and they will live for many minutes (even for an entire game, infrequently).
They add to the total number of wards you can have on the map at any one time. You can only have three green wards placed on the map at once, and only one control ward on the map at once... but therefore you can have four total wards down at any one moment if you've placed a control ward.
You can buy them. This might seem like a downside, but for champions without a support/warding item, the only access to vision comes from your trinket and its internal cooldown. On the other hand, you can buy a control ward at any time.
You might want a different trinket. It's common for junglers and solo laners to switch their trinket to the sweeper in order to remove enemy wards. If you have a sweeper and don't have a support/warding item, control wards are the only wards you have access to.
To try to answer the spirit of your original question: you should "always" buy and use control wards. Sure, sometimes you won't have a spare 75 gold, or sometimes you'll already have a control ward on the map in a good spot... but if you don't have a control ward down somewhere, you should strongly consider buying one and dropping it somewhere you care about.