So I do alright warding in the beginning with my trinket, and I know where to place wards. My problem comes as we progress later and later in the game and who should ward where and who should sweep for wards.
Next, question is do you keep an equipment spot free late game so that you can continue to buy wards?
I wouldn't really keep a slot free, per se, but with the change in the latest patch, the upgraded trinket will generate charges.
If you're a support, you can get a 
to keep warding. Hell, on some junglers I'll get it and sell it lategame. Vision is always a great thing.
thats a good question. when it comes to late game and you're at full build how are you supposed to keep warding when all you have is a trinket? Even then you might only have the red or blue. So then all you have is a support with sightstone (maybe) and 2 people with a warding trinket?
If you are not a support and your team needs more vision, get an upgraded ward trinket. Riot has been buffing it, and you can now keep 3 wards out with the stealth totem upgrade. And it only costs 250 gold.
Ward baron, ward dragon (when those are up but your team is not ready to take them), ward the area where fighting is likely to occur, ward areas where your team is looking for out of position enemies to pick off.
Buy a pink. If you have a pink on the map you should be golden to be trinket + pink once you get full build. Definitely upgrade your trinket with the new upgrade buffs as it'll give you plenty of warding. If you have an 'open slot' and you don't have a pink on the map, buy that. If not my advice is to always use an open slot for HP pots. Before you take any damage (aka enter a fight, start baron/dragon) you should pop a pot because the increase health regen applied before being hit by DoT can be a huge lifesaver. The amount of times don't die to ignite because my HP pot was running first for that buffer is too many to count.
As a support who often runs Sightstone, I make my wards land where we're currently fighting. If you're top, fighting in mid, I place my wards all on the left side of the jungle to ensure feasible escape. If we're bottom fighting mid, I run them to the right side of the jungle. I often keep the mentality of placing wards where we are currently fighting the most. I feel wards need to provide escapabilty first, then vision of the enemy team second. Ward early on your way into battle, so if you need to fall back you have clear vision of where the enemy team is or isnt.
