So you want to eschew the boring, mundane tactics of guns and be the ultimate biotic warrior?
The Adept is the Jedi of Mass Effect, except you don't get a flashy lightsaber, capable of taking out enemies with sheer force of biotic power. They're restricted to heavy weapons, submachine guns and pistols, but who needs them when you can win without firing a single shot?
If you plan to play the Adept with an emphasis on powers over guns, then put points into Biotic Mastery and pick Nemesis, which emphasizes lower recharge times and extra damage with powers. Bastion increases the duration of abilities, but the only abilities that have duration are Pull and Singularity. However, you really don't want to turn your back on that enemy you just Pulled behind you, and you'll want to detonate that Singularity as soon as possible and concentrate on the rest of the enemies.
The Adept's only weakness is a lack of tech attacks, so in order to get past an enemy's shields, you need to learn Energy Drain from Tali'Zorah once you finish her loyalty mission, use a squadmate's Overload, or damage them with rapid-fire guns like an SMG.
Depending on the difficulty of play selected, most enemies will have shields or barriers, so these protections must be removed before most powers can affect them.
Powers: Warp: The 'bread and butter' ability of the Adept, it can stop regeneration in enemies like krogan or vorcha, damage armor and biotic barriers, and detonate enemies already caught in another biotic power, like Singularity or Pull Field.
Pull: Like it says, this power pulls enemies off their feet towards you.
Shockwave: A power that travels in a straight line, knocking enemies into the air as it travels forward -- much like bowling.
"Throw": The opposite of Pull, this power pushes an enemy away; with the right positioning, it's possible to Throw them off edges and out of windows.
Strategies for specific enemies:
Husks Husks are annoying enemies, usually sent in as cannon fodder with other types, like Scions or Collectors, who have long-range attacks. They can easily swarm you, knocking you out of cover, and they move erratically, making it hard for you to draw a bead on them.
With the right positioning, when faced with an unrelenting wave of husks, the Adept can kill them all with a single Shockwave. The Adept's Singularity will also kill them, if placed in a strategic bottleneck, like a door.
There is a different type of husk that is red and looks like it's on fire -- don't let these things get close, or they'll explode and destroy your shields. Use Warp, or a squadmate's Incinerate (Mordin), Inferno Grenade (Zaeed), to ignite them -- preferably while it's in the middle of its brethren, so it can act like a frag grenade and kill those near it.
On Normal difficulty, most geth enemies have no shields, but some of the more elite and larger units, like the Geth Prime, have shields, or both shields and armor. Use Tali'Zorah's Energy Drain, in the form of her unlocked attack or the bonus power (only available to new game+ or imported Shepards), Overload (Miranda, Kasumi, Garrus), or Disruptor Ammo (Zaeed) to strip them. Once the shields have been destroyed, use Warp to damage armor, if any.
These enemies that resemble pustules with legs need to be dealt with at long range, because they have a devastating melee attack if you get too close. They have armor in place of health, so stay in cover and use Warp on them.
These attack from long-range with guns, and depending on difficulty, either have no defenses, or have a protective barrier and/or armor that must be removed with Warp.
You would think they can be dealt with like any other gun-using enemy, but they can be 'possessed' by the Collector General/Harbinger, turning them into a powerful biotic, protected by both a barrier and armor. Fortunately, only one appears at a time, and they are initially vulnerable as it rises out of cover as it transforms. They have a powerful long-range attack that can knock you out of cover, so be careful!
One of the most powerful enemies in the game, even more dangerous than a possessed Collector or a gunship, these enemies will usually focus exclusively on Shepard. They have a powerful beam attack that can destroy your shields in a second, a melee attack that does the same, armor, and a barrier that comes up when its health has been whittled down at quarter intervals.
Fortunately, you only ever encounter two! It can fly, so its beam attacks can reach you once it's close enough, even if you're behind cover. Be mobile, use Warp on the run, and don't ever let it get close. There is cover that it can't fly over, so lead it on a merry-go-round chase.
There are quite a few mercenary bands you can encounter: Blue Suns, Eclipse, Blood Pack. Each group puts emphasis on certain attacks.
Blue Suns: You will encounter enemies with rocket launchers, shields, and mechs. Stay in cover, destroy their shields, and use Singularity to pull them out of their hiding places.
Eclipse: There are engineers and other biotics to contend with, so beware! Engineers like to throw combat drones at you, which can knock you out of cover, so make sure you get them before they get you! They also like to send mechs at you.
Blood Pack: Considering how their armor can be destroyed by fire, the Krogan and Vorcha love their flamethrowers. If you have a squad-mate with Overload, use it on those pyros before they get up close and personal, and they'll explode quite satisfactorily. Krogan can charge you if you let them get close, so destroy their armor fast with Warp, and control them with Pull, Singularity, or Throw them off a convenient ledge.
Some use rocket launchers, so watch out for those missiles.