Skeletal Swing should be used on cooldown in teamfights and during waveclearing. Versus heroes, be sure your target is in range. One of the easiest mistakes to fix as Leoric is swinging at targets too far away.

Drain Hope should be used on cooldown if you think you are going to get at least half of its duration off. The animation is slow, so be sure to pick nearby, easy to hit targets. In teamfights, aim for nearby tanks to ensure maximum effectiveness.

Wraith Walk is your escape, chase and damage mitigation (with Hardened Bones). DO NOT OVERCHASE WITH THIS ABILITY. For example, their Valla has been bursted to very low health, but manages to escape. You chase with Wraith Walk, you get kited by Valla, their Uther heals her, you get bursted down. Meanwhile, you've completely abandoned your team, who proceed to get destroyed by Muradin and Arthas. THIS IS THE MOST IMPORTANT THING IN REGARDS TO PLAYING LEORIC. JUST BECAUSE YOU CAN OVEREXTEND DOES NOT MEAN YOU SHOULD. In the previous example, you could stay with your team, help kill their tanks while Uther's heals are on cooldown and Valla is playing cautiously.

Undying is Leoric's signature ability. However, like Wraith Walk, just because it is available does not mean you should force yourself to use it. Never die for nothing. Examples of good deaths are delaying for your team to capture an objective, securing a kill, saving a teammate. Examples of bad deaths are damaging an enemy to half health and then being blown up by their team.

March of the Black King is fairly straightforward. Use it when you're around half life on clumped enemies or use it as extra burst to eliminate a CC'd squishy target.

Entomb should be used to isolate squishy targets without escapes. Its use is rather similar to Tassadar's Force Wall.

During the early game roam for Reanimation stacks. If necessary, cover lanes.
The rest of the game you are an offtank. That means finding a balance between protecting your squishies and diving theirs. If in doubt, protect yours. Remember, you do significantly more damage to tanks due to Drain Hope and Spectral Leech.

Do not be afraid to die, but do not give free kills either.

Level One
You are reducing your winrate by 10% by taking anything but Reanimation.

Level Four
Fealty Unto Death is an fantastic substitute and what I used for a long time. Use it if you need more sustain. Hardened Bones is the best against burst.

Level Seven
Since Ossein Renewal was nerfed, I have started using Paralyzing Rage. Ossein Renewal is still an acceptable talent, especially if you are the only tank.

Level Ten
March of the Black King is a personal Ancestral Healing. Use it, love it.
Entomb is an acceptable substitute if you have strong followup, especially if you are offtanking. This is a risky pick in soloq.

Level Thirteen
Crushing Hope can be taken here if the enemy team has several high health targets. I still prefer Burning Rage.

Level Sixteen
I prefer Renewed Swing. Although it does half damage, it applies the full slow, which is increased by the level 7 talent Paralyzing Rage. However Consume Vitality and Imposing Presence are also solid picks against ability and auto attack damage, respectively.

Level Twenty
Spectral Leech is a ridiculously good talent. Even with his slow attack speed, Leoric will shred anyone with it.
If you are maintanking, or the enemy team has massive burst, Hardened Shield is a solid pick. I do not really recommend this, Spectral Leech is simply too good.