Dota 2, just end up permanently CC'd in every single fight.
I really just don't understand how to be relevant in this game. I can do all the farming I want but the enemy team will still be many levels ahead of me and easily do twice or triple my damage.
Step 1: Blame your team.
Step 2: Learn some Russian or Portuguese in order to blame your team better.
So, despite the word's origin and face value, the team's "carry" is really never meant to operate alone. Except in extreme circumstances, you are
not the one who is supposed to lead the charge into the enemy midst, and you are
not supposed to go bravely venturing where no teammate has gone before behind enemy lines. You are supposed to be safe, get fat, and be the hammer to your team's anvil.
You need initiators to start the fight by jumping in and either eating the enemy team's first few precious stuns or by stunning the fuck out of everyone to prevent them from doing that. Then you need some kind of followup to help pin and dismantle the team once the initiator has done their job of buying time.
Then the carry goes in and starts eating the trussed-up piñatas that the enemy team has been turned into.
This is the optimal situation, and the one you should always try and aim for. If the enemy team is halfway competent or if your team isn't quite halfway competent, this likely won't be what actually happens, but it's still a good metric to try and follow.
Also,
buy a goddamn BKB. If you do not have a BKB, you are not built yet. If you are not built yet, why are you fighting? Pre-built carry interaction should only be done very carefully and with good coordination with your teammates. Most carries simply cannot meaningfully contribute until they hit their sweet spot of gear and levels, so you getting into fights before then had better only be because your team is spoon-feeding you weakened enemy heroes so you can grow big and strong. If you're playing Antimage and your team is griping at you for not contributing in teamfights before you've even got a battlefury, they are being dorks and are likely intent on losing the game.
This does not mean you should ignore your team or refuse to help them. While you can't be expected to swing much weight around in the early game, you *can* still help out by listening to them and picking up easy kills or distracting/scaring someone trying to gank one of your supports,
so long as you do not endanger yourself. Getting a kill as a carry is considerably less important than
staying alive as a carry.
Now, I've only assumed that you're playing carry, because you're talking about damage and farming. If you are not playing a carry,
those things are not your job. There are of course roles like mid or ganker where you need a certain level advantage and a couple core items in order to hit your stride, but they're often referred to as soft or semi-carries anyways. If you're playing CM, you shouldn't be stuck in the lane trying to get last hits. You should be out supporting your team, because you do not need expensive items or even that many levels in order to be relevant.
As a general suggestion, I'd like to recommend playing some coop vs. AI rounds. That gamemode tends to draw a
slightly more chill crowd, and while the AI is hysterically predictable and dumb at times, they can still provide a good learning experience for some aspects of the game because they have
terrifying reaction speeds. If you can properly lock down a bot team with CC or beat them in last hits, you're doing well (this mainly only applies to the higher difficulty bots, the lower difficulty ones are... Not very good at anything except walking in a straight line and dying).
Also, the bots rarely taunt and jeer quite as much as an enemy human team, which can help.