Bakasana is usually the first arm balance we learn. Other contenders once you've gotten your yoga learners' permit are Bhujapidasana, Arm Pressure Pose, or, though it's not exactly an arm balance, the easier variations of Vasisthasana, Pose dedicated to the sage Vasistha, aka Side-Plank pose.
There are many ways to enter Bakasana, which is part of the reason that it's such a fun pose. Here are five ways, ranging in difficulty from Beginner to Why Would Anybody Want to Do That (WWAWDT)?
Here's a great overall Bakasana video tutorial that far exceeds what I'll write here.
1. Lift-up version I. Simple: crouch, put the shins/knees to the backs of the arms and shift the body weight until the toes get light. Generally, the wider the knees and elbows, the easier the pose. Eventually try lifting the feet (perhaps one at a time) from the floor. Faceplanting is not recommended.
2. Press-up. From a tripod headstand position. From a crouch put the head down, hands flat. Lift the feet, so just the head and hands are on the floor, knees on the backs of the arms. Now, for Bakasana, just reverse that process, shifting the weight off the head. At some point, add a strong push through the arms. Maybe only pass through Bakasana at first, ending up right back in a crouch. Sooner or later, stop and hold in the arm balance, on the hands. For extra points, start from a full tripod headstand, legs straight.
3. Jumping. The difficulty rises a few notches. Strength, control, and confidence. Here's a great tutorial specific to jumping/floating into this pose.
4. Lift up II. From seated, Ashtanga style. Lifting the legs through the arms is about strength, not arm length. That accomplished, getting the hips high enough for the knees to find the arms is crucial. A good prep is working in reverse: start in Crane and try to lower the legs (ankles crossed) through the arms to seated.
5. Lift up III. Could be called Niralamba Bakasana, Unsupported Crane pose. A lot of strength, obviously, but more technique and cunning than, say, Lolasana or Tolasana. In those poses, the center of gravity (just below the navel) is below the shoulders, so success is basically about pulling the legs into the body, off the floor. In all Bakasana variations, the center of gravity is above the shoulders, and therefore must be over the hands. Shiva himself couldn't do otherwise. In practice, this one is more like a variation on Adho Mukha Vrksasana, Downward Facing Tree Pose aka Handstand. The trouble may seem to be strength, but it's probably those damn physics. Things are entirely different without the knees anchored to the arms, and if you can't do a basic handstand, this one's not likely.
Note: Though it's not identified as a separate pose, this is used in the Ashtanga Standing Sequence. The line between yogi and masochist is hard to find, sometimes. After five breaths in Utkatasana, keep the knees bent, put the hands down and lift up. Then back to Chaturanga and...well, you know the rest.