Edit: Light heavy is dead until further notice, since heavy no longer has any anti-surround capability
Chaingun and combat pistol (Heavy starting weapons) are both pretty easy to micro. Combat pistol is simple and common among other classes, and chaingun is actually most effective when you a-move straight into the enemy. Since heavy starting weapons are so easy, I decided to make a guide for a high-level heavy with difficult equipment. In this guide I will share some of the tactics I like to use, and hopefully other heavy players can add to the discussion by posting their favorite tactics.
This guide is meant for a player who already has most of his equipment unlocked. Most of my tactics involve flamethrower, flashbang, or pistol since these are the weapons I use. I also like to use light armor (thus Dalas's Light Heavy Guide), but some of these tactics should be applicable to medium or heavy armor as well. I usually take oxygen mask too. Tactics relating to combat shield will probably be relevant whatever your equipment loadout is.
Combat Shield Usage:
While I might be biased, I think that combat shield is hands-down the best class ability in the game. Combat shield reduces damage by 75% before armor, which gives it the ability to reduce damage from any enemy (excluding monstrosity and splasher) to the minimum value of 0.5. It is nearly impossible to die from standard attacks coming through combat shield. Of course, combat shield only defends the front 90 degrees or so of your body, so positioning is key to maximizing the utility of your combat shield. When attacked (if you choose not to kite), ensure as much of your body is touching walls or sandbags as possible. Corners are best, walls will do in a pinch. It is also a good idea to position yourself thus before opening any dangerous doors. I have (true story) had to go afk before, but left my heavy with shield up in a safe corner. Sometimes I'll come back 4-5 minutes later to see a horde in the room, but my heavy will only have taken 20-30 damage because the only place zombies could attack me was through the combat shield.
New in the 0.42 update, heavy can now place up to three sandbags with a timed life of 60 seconds. This is incredibly useful! Before opening a door you can place sandbags to keep yourself safe, or you can block a corridor with bags while you reload. Sandbag placement is instant, so they can be used in almost any situation. They synergize especially well with combat shield, since you can almost block a corridor, stand in the middle of the gap, and enemies will be forced to attack you on your shield only. Their biggest disadvantage is the 60 second charge reload, which can make choosing when to use sandbags difficult.
Fighting Special Enemies:
Combat shield is very good against special enemies as well as against regular zombies. However, tactics differ depending on the enemy you are fighting. Splasher is easiest. Just equip combat shield, make sure to face the splasher, and let him run straight into you. You usually take only around 30 damage. Vs giants or mothers, its best to hunker down and shoot clip after clip of flamethrower straight at them. When fighting these enemies it's their support zombies that are most dangerous, so flashbang yourself if they start to flow around your shield. Vs soldiers, the hardest part is getting close enough to flame them without taking much damage. Try toggling shield in between their weapon shots so you can get in close, or throw a flashbang and run in while they're blinded. Once you're near a soldier, it's easy to burn them down. Titans, of course, are invulnerable to flame damage (as of .55b), and won't take much damage from your sidearms either.
Assault Rifle Hold Fire:
It's easy to stop your gun from firing, just keep moving. Combat shield, however, means that sometimes you will want to stay facing your enemy but not waste ammo shooting at them (if they're burning to death for example). It's not hard to hold fire while standing still - switch to your sidearm and spam the stop key. This should work with most other weapons as long as they have a damage point, however flamethrower will not work with this since its damage is dealt instantly.
Getting surrounded/swarmed is one of the worst things that can happen to you in a game of pandorium. Heavy is especially vulnerable, because even with light armor zerglings can still catch up to you. Turn around to shoot them and before you know it they surround you, giving time for the horde right behind to catch up. Combat shield can help in these cases, but often it's not enough to stop you from taking terminal damage. Instead, my favorite tool for escaping surrounds is the flashbang. Often players surrounded and on the verge of death will grenade themselves, dying but taking out a swarm in the process. With flashbang, you can stun all the zombies around you while giving yourself a chance to reload, shoot, or run. Your vision will be reduced, but you can still see enough to fight your way out of most surrounds before the zombies recover from the stun.
Everyone hates larva. Especially since the 0.41 update, larva can easily kill you if you get infected while far from surgery. Wearing light armor helps with this somewhat, but any bad luck/delays on your way to surgery can leave you lying on the floor with a gaping hole in your stomach. While notoriously difficult to kill before they infect you, there are a few ways to increase your odds. If you can see the outline of a cloaked larva, flashbang stuns them for long enough to run by, but you are not able to detect the larva until it jumps at you. If you don't see any larva, a-moving around with flamethrower equipped gives you a better chance of killing them. Of course, a-moving with flamethrower instead of your sidearm makes you more likely to waste ammo or deal accidental friendly fire, so it's a trade-off.
One of the best uses of flamethrower is to help your allies clear out rooms infested by cocoons or by eggs. If you burn down a cocoon or egg, the zombie/broodling inside starts out on fire as if they had been shot once by a flamethrower. This means that they will die quickly without any additional flamethrower shots. Careful of friendly fire, and make sure to angle your flamethrower shots to hit the most possible cocoons/eggs and save ammo.
Not practical (as of version .55b). Stay far away from nests, they're dangerous.
Sandbags are an excellent tool. They have many uses, but are especially handy when assaulting rooms. If you know there's a horde behind a door (motion sensor is good for this), walling the door off before you open it makes you much stronger in these situations. Keep in mind sandbags have equal target priority as yourself, so enemies - especially hydralisks - will destroy sandbags fairly fast if not killed. Since they place instantly, sandbags are also a good way to distract enemies while you reload. You don't need to wall off an entire corridor, just drop a single bag and get some distance.
Speaking of reloading, ammo boxes are an excellent way to reload flamethrower when you need it in a hurry. Placing the ammo box and using it does require you to turn however, so try to make sure enemies are flashbanged or distracted with a sandbag before you place a box, or enemies will probably damage you while your combat shield is out of position.
TLDR: don't get hit without combat shield. Spam flashbang whenever you get surrounded. Know what you can fight and what you can't.
I hope this helped! Please add any interesting tactics or information.