How do people reach T6...? I never ever came close to that. I play for some hours and I get 0 items to upgrade my stats. I lose motivation... :/
Out of curiosity, what paragon level are you? How long have you been playing with your main character?
There are 3 fairly simple steps that will help you improve your character by leaps and bounds:
1) Get a decent weapon. Not necessarily an ancient, but one with a socket (which you can enchant anyway) and decent stats/good legendary affixes.
2) Get a Ring of Royal Grandeur and 3 pieces of a given set. Most classes have sets that start to become really interesting if you have 4 pieces. That means you actually need only 3 if you do Act 1 bounties and get the RoRG through Act 1 horadric caches (which isn't hard to accomplish). The RoRG lowers the set pieces requirement needed to gain the corresponding set bonus. So with a RoRG and 3 pieces of a given set, you get the 4-piece bonus.
3) Get legendary gems. You get those with greater rifts. They're a guaranteed drop on GR bosses, even at Greaert Rift Level 1, and you can only drop a leg gem that you don't already have in your equipment or stash, meaning you'll always get the gems you want eventually. You can socket them on rings and amulets, so you can have 3 different leg gems at the same time, and trust me, they make a huge difference, more than any given stat. The trick is to open a GR Trial and leave immediately so you can start from GR1 and work your way up.
Once you do those 3 steps you should at least be able to do T3 or T4.
[EDIT] A few more tips:
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Use Kadala to gamble for equipment. You need bloodshards, and you'll get those mostly through greater rifts and bounties. Kadala has a high legendary drop rate, and you can drop any leg in the game. However, only use it for armor pieces and off-hands, not rings, amulets or weapons. Those cost too much and are too unreliable.
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Do public games with people slightly above your own character. Not too much, otherwise they'll kick you out or leave because you're slowing them down. You'll get more XP, potentially more loot if they share with you, and you'll get through rifts faster.