Warrior 3 is the trickiest one in my opinion. It deserve some perpetration poses, like eagle pose, tree pose, Uttanasana and Ardha Uttanasana (Forward bend +half forward bend).
It is a balance pose, strengthening and lengthening our legs and back. Like the first two warriors it brings our attention to 2 different directions (front and back), while shifting our balance point from perpendicular to the floor to horizontal.

Let’s break it down:

Start in mountain pose. Bring your hands to prayer position (Anjali Mudra).

Breath and think about the center balance of your body, from feet grasping the ground, up through the legs, throughout the spine, to the crown of your head. Energy flows up and down in your body in a circulation with your breath.

Slowly bring one leg up, bend both legs. Always start with bent legs, from there straight them as you can.

Shift your weight forward, straighten your back, and send the leg you lifted backward.

Straight your legs slowly whilst balancing yourself.

The full posture is when you are horizontal to the floor with one leg straight and your spine long and straight, Arms reached forward.

But let’s start with our own body abilities and take it to our limits. I like to keep hands in prayer position, it helps me reach further with the rest of my body into the posture.

Be aware that your back is long, straight and specious, forward. Keep the neck along the spine in a straight line. Keep the leg backward also straight and strong (all muscles activated).
Engage your core, it is helpful in balance postures and it will activate your upward flying lock (Uddiyana Bandha). I explain about the bandhas here https://goo.gl/DsKbGQ.

Your gaze (drishti) is focused lightly straight with the inclination of your head.
Think about the new balance point you are bringing to your body with this movement. It is great that we move our body to all its range of movement, and that we are changing perspective from time to time.

In the video you will see, me too struggle with warrior sometimes. Especially in my left side. We usually a-symetric in our body, we also have muscle imbalance. It is natural.
Normally you will notice in your practice which side of you is stronger, which is more flexible. You will find it harder in some sides.

Don’t forget to try this at home ;)