How can I animate this?

I am trying to figure out how to animate a sword appearing out of thin air, very similar to 0:55 in this video below.

Well, the base mesh looks like it is an animated transparency with a glow to hide the transition, then it has a swirly energy haze around it, Which I would try to create with a smoke sim and an emissive shader.

Oh my… That sounds a bit complex. Are there any tutorials that could teach me that?

You’re looking at reproducing an effect that was produced for a big budget film. it probably took several artists several days just for that effect. It’s gonna be a little complex. Total man-hours on a CG production of this scale can be in the neighborhood of 5 days per second of animation. Those 50 frames of that sword fading in represent about 2 weeks of work.

CG is a lot of work! but it’s all learnable and doable, it just takes some practice and patience.

This is a tutorial with a cool dissolve effect, you might be able to apply some of the techniques in reverse to get a fade in effect: