Alaias float way less than your standard shortboard, you're pretty much immersed while paddling and rather need to balance your body like swimmers.
Use your core muscles to keep your body straight in line.
More than muscle power, hydrodynamic and fluid movements are essential. The first times are exhausting because the body's position is wrong.
Once you get it right it's really pleasant and it's even less traumatic for your back than conventional surfing. The more you arch your back the more you sink.
Think crawl swimming, relax, forget the board, it will naturally stick to your body and follow you.
By stretching out your arms forward, each stroke doesn't only propulse you, but also lifts you upward.
Duck diving, You can push the alaia way deeper than any standard board. Underwater it pretty much reacts like a wing. You can control it and swim under the wave.

Taking off

Sit, you sink down to your shoulders. The fastest way to get back to the surface and generate speed for take off is to give a few breaststroke swimming mouvements with your legs.
Timing is essential. Think bodysurfing. Train without a board first to get the feeling.
Swim in the face of the wave using arms and legs.
Project yourself down the face.
Keep your body in line, position yourself further forward on the board and push down with your chest while paddling.

Riding /Trimming / Gliding

The riding technique is quite different from a board with fins. It's very similar to riding a snowboard in deep powder.
The edge of the board is the fin. By digging it in the wave the alaia trims across down the line.
By releasing it, the board slides sideways.
Like snowboarding, your chest shows the direction and the board follows.
Alaias are extremely sensitive, you ought to ride crouching to lower your gravity center and keep your hands close to the water for more control.
Though Alaias don't float much, their hydrodinamic properties are excellent, the drag is minimal and the planing ratio optimum.
Put in movement, the kinetic energy generated by the water flow, lifts the board right away.
They plane and glide down the line faster and longer than any other boards.

Not used to control the ride with the rail, beginners have difficulties keeping the board in line and won't stop sliding sideways.
In this case, move your gravity centre above your back foot. By doing so, the tail cuts in the face of the wave and you can control the slide.