The easiest thing is, look Video Guides from Genji coaches about this (they are free avaiable on youtube).
I can sum up some important things.
Know the time to use it.
(For examble when enemy Zen, Baptise, Moira, etc. has important counter on cooldown)
Know the position of your enemys before.
One of the most important one: Know the DMG numbers you need to kill someone with swings and dash. There are big differences in how many hits you need to kill someone while Solo Blade, Mercy buffed Blade and Nano Blade.
That kill resets are important to start a chain reaction.
If you don’t use double jump before and fall down to an enemy, you can double jump in air during blade to avoide sleep darts. This is increddible effective.
Wait for enemies to use whatever ability they have that would shut you down before you ult, like sleep dart, gravitic flux, trans, etc.
You can kill a Pharah with DragonBlade if you dash up to her after she uses jump jet, ult for the second dash to get in close, and then use your double jump to extend your air time to get the two swings in.
With nanoblade, you can kill if enemy Zen uses Trans by dashing immediately after the slash damage. Much easier for Ana to just anti-nade them though.
Im no genji main but I have success going after the 200hp targets first, if you see a target with 200hp and has no stuns then that should be your very first target. Zen is a perfect example, soldier, hanzo, widow etc. the only thing you have to really consider is baiting their mobility, for example if you are after a moira, simply close the gap and slash her once, as soon as she fades, you can now dash towards her. Genji by default moves slightly faster than most heroes so a mcree simply moving backwards wont mean you wasted the ult.
Remember genji also has like 6 seconds in ult so thats plenty of time to get a few kills, you dont always need a massive team wipe, just killing 2-3 is more than enough to win a fight granted you went after the right targets.
Ah, let professor Shock teach you the ways of Genji blade…
Step 1: Watch Necros Stream 24/7
Step 2: Practice 180 flicks every time you play the game
Step 3: Improve your reaction speed
Step 4: Use the Hanamaru Code to practice blade
Oh. It just comes with practice. I sucked at first using Genji blade as well. But I continued to practice custom lobbies with Ana bots and repeatedly blade. Eventually, I got a hang of it.
I forgot to add one more thing. Another alternative to get gud with genji blades:
Have your team die.
Play an anime opening song.
Blade into a 1v6.
Remember to put your mic near the keyboard when blading.
Die.
Blame your team and report.
Profit.
Some have already offered good advice, but I’ll offer my two cents.
Target priority. Focus the one with lowest HP first, then move onto squishies. The initial activation of Dragonblade is where you’re most likely to be countered, considering none of your actions are usable initially.
If your low-HP target is bubbled or otherwise defended, move to the next target. Staying on target will burn time off your Blade, and you can come back for the kill after.
As an addendum, if someone is ulting, focus them carefully. Coalescence, Valkyrie, Rip-tire, TAC-Visor, etc. Take care when you focus them; if you lose the fight, your team will be down an ult and a player, and the enemy will only be down an ult. Try not to duel with Deadeye - if it’s not a Nanoblade, by the time you’ve almost killed him, he will be charged and probably shooting you.
Practice. If it’s a Nanoblade, practice your dash+slash. If it’s a Dragonblade, practice your slash+dash+slash. Practice your combos; your dashes; potential escape routes if you need them. It’s good to have a fallback if your Blade goes south.
Keep moving. Whether it’s sporadic single-jumps, double-jumps, strafing, etc. etc., keep it random and unpredictable. Genji is hardest to hit when he’s using his mobility to the fullest extent. As Conker said earlier, you can store your double-jump until after Blade is out to dodge Sleep-Darts, Graviton-Surges, Earthshatters, Flashbangs, etc.
Wait out enemy Ultimates. Transcendence, Sound-Barrier, Graviton-Surge, etc. You can usually force them out if they know you have Blade by dashing in, or dashing up.
Take note of enemy positions. Ideally, your opponents would all be grouped up, but that won’t always be the case. Being able to effectively dash between targets is important.
Do not blame yourself if it’s not a 3k or 4k. Dragonblade is a powerful ultimate with many downsides. Confirming even two kills will still turn the tide in your team’s favor, especially if it’s their healers, the lifeline of the composition. It’s easy to feel as though it’s not enough, but it is.