The Vanguard is high-risk high-reward combat oriented biotic. While the Vanguard may not have the total biotic control of the Adept, the Vanguard can lay out tough opponents with flash and guts.
The Vanguard cannot initially use an assault rifle, but picking up the assault rifle upgrade at the Collector ship will make the Vanguard even deadlier than he already is.
The first goal of any Vanguard is to wipe out any shields, barriers, or armor of the opponents in the room, the Tempest, Collector Assault Rifle, or Geth Pulse rifle work very well with the Vanguard. Using Cryo ammo to freeze the enemy after wiping said defenses will leave the enemy open for a biotic charge followed up with a point blank blast from a shotgun.
Another option is to use shock-wave to knock the enemy back and follow this up with the biotic charge/shotgun blast that makes up the bread and butter combo for any Vanguard.
Another effective strategy is to learn the Neural Shock ability to stun enemies, and again, go in for the charge and shotgun blast.
As for your comrades, Garrus and Mordin fill out missing tech gaps for a more balanced squad, as Garrus can snipe from the distance or become a dangerous tank with an assault rife, while Mordin's incinerate can wear down tougher opponents, and his cryo freeze offers the perfect set up for the biotic charge and point-blank shotgun blast.
Two other strong teammates are Grunt and Thane. Grunt becomes the perfect tank, able to draw attention away from both the Vanguard and Thane. Thane meanwhile, can use biotics to wear down opponents and snipe from far away. During the confusion caused by these two, the Vanguard has a perfect opportunity to charge in with guns blazing and unleash a full clip of cryo ammo among the enemies, which Grunt can then clean up.
The Vanguard plays high-risk, high-reward, and with the proper weapon load-out and teammates, no one can stand toe to toe with a charging biotic.