My strategy for being a Vanguard.
This is assuming you are on your first play-through
You need to be conservative with your ammo, wasting all of your shotgun shells on that one Colossus might seem like a good idea until you run head long into multiple Husks. Learn to whittle your foes down with your pistol or smg before whipping out your shotgun.
Never wait to use your powers, at the same time, don't use them the second your cool down ends
Always keep an eye on the battlefield. How many enemies remain? Where is there cover you can use while on the offensive? If you charge are you going to be exposed?
It's a good idea to keep a teammate with inferno ammo and/or Warp ammo, if you don't have them. Shotguns do a lot of damage to shields and barriers but not nearly enough to armor. On harder difficulties where foes can have multiple layers of armor before you even reach their health, this is a must.
This is the reason I play as a vanguard
Charging is the signature move of the Vanguard. Charging to and fro in a burst of blue light, like Sonic the Hedgehog with a shotgun. Charging can be a very helpful maneuver, however, It can also land you in a world of hurt.
-Never charge directly into a large group, this should be obvious but still needed to be said. Chances are, even on lower difficulties, charging headlong into a medium to large size group of enemies will end with your intestines laying on the floor.
-Always have your shotgun out. If you are going to charge into the firefight, whip that shotgun out and shove it down the foes throat before you pull the trigger. As stated above make sure you have an ammo power active depending on what kind of barriers you are going against. Shotguns overwhelm Barriers and shields with the amount of pellets they spray but don't have the penetration to do any damage to armor.
-Use your teams powers. Engineers to take down shields and armor and biotics to toss people around once the protection of their shields and armor are gone.
Push and Pull
Always try to knock your foes off any platform they may be standing on.
If anything else it will get them onto the same level you are on. Best Case scenario they fall to their deaths and leave you with one less headache.
If someone is far away pull them towards you, This will likely end with them falling into a "bottomless pit" to their deaths. If there is someone at a mid range but you see a pit behind them or off to the side angle your push to send them over the edge to a similar fate.
As this stuff is few and far between, its best to save it for either a very large group of enemies such as Husks or one big baddie such as a Scion. Never waste the ammo on a singular enemy where your teammates can easily finish him off.