In order to best play the Vanguard, one must master their deadly blend of close-range skills with biotics.
The Vanguards class-skill 'Biotic Charge' will prove to be your bread and butter over the course of the game. In order to best utilize this power, you will need to be able to quickly bring down your enemies biotic barriers, tech shields and armor.
For this reason I highly recommend putting skill points into 'Incendiary Ammo' early on. The damage increase against armored foes can prove invaluable. Bringing along companions with 'Overload' or 'Warp' (Miranda, Garrus, Thane) can help compensate for the Vanguard's deficiency in dealing with those armor types. Mid-game upon receiving the additional weapon specialization, the assault rifle should be an easy choice. Bringing the Vanguard a much higher damage output at longer range, it will allow you to quickly pick off enemies your shotgun or heavy pistol would be unable to.After draining your enemies defenses, switch to your shotgun and use 'Biotic Charge' to get up close and easily clear large groups of enemies. 'Shockwave' can prove useful in blasting weakened enemies from a distance off the map.
The Vanguards loyalty power will prove to be an important part of your play style as well. As your 'Biotic Charge' will find you in the front lines very often, mastering Jacob's 'Barrier', Legion's 'Geth Shield Boost' or Grunt's 'Fortification' can frequently save your life. Deploying these powers after taking damage can effectively serve as a 'heal', quickly replenishing Shepard's shield in times of need. Should you find yourself seeking an offensive loyalty power, Samara's 'Reave' can effectively immobilize and damage groups of enemies, while also replenishing Shepard's health (if the enemies are organics).