Systems & improving
Arcana/battle-skill basics, mistakes and a checklist
Mechanics to Learn First
Arcana：Stat boosts you set up before a match. Start with the "recommended" preset the game suggests, and once your Arcana level passes 5 you can start swapping them out yourself.
Battle Skills：You choose a single battle skill (unlike LoL, you can't carry two). Flash (a short-range warp) is the standard for most roles. Jungle needs Smite (deals heavy damage to neutral monsters to secure them); the Marksman often takes Heal (restores HP and boosts allies' movement speed) or Purify, and Roam takes Sprint.
Recommended Items：Press and hold a shop tab to see the build the game suggests. Follow it for your first 10 to 20 matches, and once you're comfortable, start adjusting it to counter your opponents.
Jungle Buffs：There are two colors. The red buff adds damage over time and true damage; the blue buff gives cooldown reduction and mana recovery. If a color isn't useful to you, it's fine to take the other one instead.
Vision：Securing vision (wards) is the Roam's key job. Place them before you go to contest an objective, not after the fight has already started.
Five Common Beginner Mistakes
Pushing the lane without vision：In HoK, the river is the path ganks come through. If your jungler or mid laner has been off the minimap for more than 5 seconds, back away from the minion wave right away. Step into the bush to check before you commit.
Fighting under your own tower：HoK towers deal modest damage per hit, but once that first hit lands you melt fast. When your HP is low, don't dive in or get dived; recall and reset instead.
Ignoring the Tyrant and Overlord：The Tyrant and Overlord (both around 4 minutes) give your whole team powerful buffs. Watch the timer at the top of the screen and go take them together with your teammates.
Going full-damage builds on Assassins and Fighters：HoK matches are decided in 15 to 20 minutes. Make your fourth item almost always a defensive one (Spikemail to counter physical damage, Succubus Cloak to counter magic, and the like), because enemy damage is extremely high in late-game team fights.
Not buying boots：Movement and roam boots are cheap and apply a lot of pressure. On any hero, buy them early, by the 2:30 mark.
First 30 Matches Checklist
Matches 1-5：Tutorial and AI matches. Learn to navigate the shop menus and get a feel for landing the last hit on minions.
Matches 6-15：Casual 5v5. Pick one hero from the recommendations above and keep playing that hero.
Matches 16-25：Stick with the same hero. Build the habit of checking the minimap once every 3 seconds, and buy boots by 2:30 every match.
Matches 26-30：Ranked unlocks (account level 7). Start with Quick Match. Games are shorter, so leads are less likely to snowball out of control.
Beyond that：From match 30 on, dig into the matchup notes and counters on your hero's page. Also start paying attention to picking your second item based on your opponents.