Once More Unto the Breach!
Or, A Young Vanguard's Primer on the Proper Disregard for Personal Safety
The first lesson to properly using Charge is to Upgrade Charge. The ability really feels very weak at low ranks because it's not until you've upgraded it that you get the tools you need to survive its usage. At low levels, Charge is basically a finishing move. You can use it to pick off isolated foes who have cut themselves off from their allies, or to reposition Shepard into a new strategic spot from which to take cover. Both of those are very good ways to use Charge throughout the game, but it's not until you've picked up a couple of ranks that you can use Charge with abandon. In particular, Rank 2, which reduces the recharge time by 25%, and Rank 6, which gives Charge a 25% chance to not trigger a cooldown, or adds a substantial boost to your shields after charging are really really important.
The second lesson to properly using Charge is, like Alec Baldwin says, to A. B. C. Always Be Charging. If Charge isn't on cooldown, and you aren't in cover, you're dead. If Charge is on cooldown, it's because you've just charged, which reset your shields to full and knocked whatever you charged at into the air. Your goal, in the time between Charging and the cooldown on Charge ending, is to kill whatever you charged at, and then either get to cover, or pick a new target to Charge at. This is where upgrading to Rank 2 comes in, as does managing your weight capacity. Travel light to minimize your power recharge time. As a Vanguard, you'll primarily be relying on your Biotic Powers, your Melee attacks, and a trusty Shotgun - don't bother trying to haul around an Assault or Sniper Rifle, and you could make a convincing case for even skipping an SMG or Pistol once you get the hang of things - who needs more ways to shoot things when you can ram your fist into their face at the speed of sound?
The third lesson to properly using Charge is Pick Your Targets. As noted above, early on, you'll primarily want to use Charge on three types of targets: Enemies occupying strong defensive positions that you would rather have for yourself; Enemies that have cut themselves off from their allies and whom you can pick off while your squad mates keep their friends busy; and the last few enemies from a large group once you've thinned their ranks a bit. As you get better at Charging, you'll learn to spot enemies standing on the 'wrong' side of cover which you can use while waiting on your Charge cooldown, as well as which enemies can be killed within the stagger of a well placed Charge->Nova->Melee or Charge->Shotgun to the Face combo.
The fourth lesson to getting the most out of getting up in your opponents' faces is Combine Your Powers. Like the Planeteers, you are at your best when your squad uses their powers to support you. A well placed Singularity from Liara can present you with a field of unwitting chumps to Charge into and punch repeatedly into submission. A properly timed Sabotage can leave a clump of Synthetic foes fighting amongst themselves while you wreak havoc. Other squadmates can send out Decoys or Combat Drones that can draw fire while you Charge in. The longer it takes your opponents to realize that you are what they need to be shooting at, the less time they will spend shooting you before Charge comes off cooldown and you can recharge your shields.
The fifth lesson is Detonate! Charge is a universal Detonator. What does that mean? That means that if you can land a killing blow with Charge on a target suffering from any debuff, it will cause an explosion doing massive damage to nearby enemies. Better yet, if you do it to a frozen foe, or one that's on fire, you'll cause everyone nearby to freeze or catch fire. And when a Cerberus Merc is on fire, he isn't shooting at you. When a Geth Trooper is frozen, he'll shatter from the next shot he takes. Charging into a target stunned by Overload or Disruptor ammo will do large amounts of damage to other shielded foes in the area. Comboing with other biotic and tech powers is particularly handy for two reasons; first off, Biotic + Biotic and Biotic + Tech combos don't need to be a killing blow to detonate. Even better, as a Vanguard, you can invest one talent point into Pull to start the chain reaction yourself, meaning you don't even need to rely on your squad. Still, don't rule out the value of Cryo and Fire explosions - the former is quite easy to set up yourself thanks to Cryo Ammo. Better yet, take the Squad Ammo upgrade, and let your allies set up Cryo explosions for you. Every frozen opponent you kill with charge will freeze all of it's allies nearby!
The sixth lesson is Get in Fast. One of the biggest disadvantages of Charge is that it sends you right into the enemies face, all the way on the opposite side of the battlefield. Unfortunately, if they've fortified themselves, taken cover, and spread out, getting in one bad dudes face means there's probably six others taking potshots at your back. But!, One of the biggest advantages of Charge is that it sends you right into the enemies face, all the way on the opposite side of the battlefield. And if you do it before they have a chance to take cover, you can wreak havoc. Groups of AI enemies do tend to start out with a 'plan' - the game tends to give them pretty good defensive positions to work with, and the AI knows about them. But no plan survives contact with the enemy, and what is Charge but very forceful contact with the enemy? Combined with a well placed primer like Singularity or Overload from an ally, you can hit an entire squad of opponents as they come down from a dropship or in a narrow chokepoint before they reach cover. This is devastating.
The final lesson you need to learn with Charge is to Finish What You Start. Very few foes should be able to survive a Charge combo. If most of your foes are surviving it, you should probably work on softening them up a bit more from range before Charging in. Whether you prefer to follow up your Charges with Shotgun blasts, Melee attacks, or Biotic Powers (particularly Nova) is up to you, and will determine how you upgrade the power, but the key is that after Charging at an opponent (or group of opponents), you should have a plan in place to dispose of them or get to safety after having done your damage. I find it's really helpful to slam on the Shift key just as my Charge makes impact to take a moment to aim, assess my available targets and cover opportunities, and plan my next few seconds of action until Charge comes off cooldown again.
Beyond that, it's really just a matter of practice, levelling up for more Charge upgrades, and buying whatever passive defense upgrades - particularly to shield strength - you can get your hands on. The stronger your barrier, the stronger your Novas, and the longer you'll last between Charges, so anything that improves Shepard's Shields is a very good investment for a Vanguard.
Best Answer
Your initial thoughts are correct about the armor. This link describes how to kill a brute and offers a brief video with some general info.
http://www.ign.com/wikis/mass-effect-3/Brute
Brute's defenses consist entirely of a yellow Armor bar. To deplete this you can use fire-based attacks and Powers meant to reduce armor. The most important thing to remember is to keep your distance. Stay behind cover and roll out of the way when it nears you. If it hits you, your shields will evaporate. Hit it with Grenades and other explosives. Armor Piercing Rounds and Disrupter Ammo are good to help reduce the armor, but explosives can momentarily pause the creature, giving you valuable time to get away.
The other thing I've been doing a lot is saving my grenades for large enemies and bosses only. I've really only had to deal with brutes and atlases so far, but having grenades while your other abilities are in cooldown makes a big difference.