What is a good method for constructing dirt jumps?
Jumps takes time and effort to do right.   If you're going to rush or do a half-arse job then don't even bother starting.

Design is important - you need to consider run up space before and run out space afterwards.   Make the jump wide enough to give options - a metre would be a fair width unless you're making it difficult on purpose.

Bailing-out options - riders will ride around if it looks too hard, you may make the jump really wide to reduce this, or make it longer to go around.

Try to avoid digging a moat around your jump.  Source the dirt from metres further away, you want to avoid having water collect on your track, because wheels and water means erosion.

You're aiming for a smooth curve on the face, so build up your jump a few inches then stomp or compact it.  Damp soil will compact better than dry.

Deeper inside the mound you can use big rocks for bulk, but still pack the soil around them.   Trees and wood is not so good, it will rot.   Tanalised timber is okay for surfacing.

As your jump rises, keep tamping it down.  Use water to dampen it.  

Remember it doesn't all have to be built in one sitting.

You can use shingle/stones to help reinforce the surface, but don't put sharp edges facing up.  Big flat river stones are okay in moderation.

The top - I'm not so sure on this.  You want to curve it back down quicker than you went up, but you must not have a lip or a sharp edge.... it won't last.   Jury is still out on timber at the top.... if you were building a jump with a wall on the far side (ie you have to get off the ground) then timber supports will be required.

The danger of timber is wear over time may create a tyre-grabbing rut right before the edge, where it's too late to stop.

Finishing - use a watering can or hose with a shower spray to smooth off the surface.  A flat spade or rake may be useful for smoothing, or you could even use a garden roller.   Also you might want to use some matting or concrete pavers to minimise erosion and to assist traction.

Final thought - do get permission to do what you want to.   Or do it on your own land.   Don't go damaging trees or wrecking other things to make your jump.



Edit: I forgot to add maintenance.   Do periodic work on your jumps, to fill erosion or ruts, or just generally clean up.  Rubbish laying about attracts other rubbish so keep it pleasant.