Start small and make small goals... focus on 1 thing at a time such as keeping Slice&Dice up, &always have it up before you burst/shadow dance. Make sure when you dance you pool your energy, don't dance if you're energy starved.
Read your passives.
Make good key bindings, and get the best macros, most macros now just tend to be focus. just repeatedly use them until you become comfortable& confident with your binds , abilities, and macros.
Get the correct gear, and stat priority and understand why.
Learn how to deal damage correctly.
Learn the diminishing returns tables and what classes that DR certain abilities/CC with yours.
I suggest not jumping straight into rated arena. You're better off queueing skirmishes and getting random partners, it will help you learn the other classes , and expose you to different levels of players.. also it'll help you find partners, & not limit you to that 1 partner repeatedly queueing rated games that is the same caliber as you.
Watch your buffs/procs, and work around them and watch the opposing teams players buffs/procs and react.
Just play ahead and use your cc and burst early.. in the current meta if you fall behind and your team runs out cd's and you're having to peel.. chances are you've already lost or about to lose. Check 3v3 ladders, and follow what the current top rogues are enchanting/gearing/talents/glyphs.