As above, it can be dirt cheap to build a scraped line in the dirt, or it can be fantastically expensive to build a durable line in a swamp. £20 per metre was the number bruited about for Kirroughtree but then it seems to be mostly in excellent ground, and FC have advantages in terms of land ownership and access, hardware, and their own quarries.
Also depends what you're making... One major reason jumps-and-pumps style trails are so popular is that you can smash them in with a big 360 and a good driver, for example, massive smiles per hour... but handbuilding them is a nightmare, so much material to move. Meanwhile natural-feeling armoured singletrack is much harder to build, because you have to retain and work around existing ground features- can't do it with a big bucket, and no matter what there'll be handwork. And relatively lightly built or as-dug trails are quicker, and tend to feel nicer, but unless you have perfect dirt tend not to last too well either.
Construction methods... Vary depending on circumstances- how longlasting it has to be, how much traffic, ground conditions, and target market. But the stuff I know best is handbuilt, very busy trailcentre stuff and it goes like this:
Dig "tray" around 2-3 foot wide, going down to good solid mineral soil- you remove the topsoil with its high organic content basically because it holds water and it's squishy, you can't build anything durable with it and you really don't want to build on it. That can mean going down quite a long way. You dig around roots etc so that they're left suspended- basically you want to remove anything that isn't solid.
At this point, depending on the ground and the lie of the trail you might also be putting in some serious drains- sometimes the only option is culverts under the trail, but you avoid that if you can. So big topside drain, pipe laid as low as you can. (sometimes some alternative methods, but let's not get too complicated)
You'll now have something that looks a wee bit like a trail. You bury this... We use mostly crushed rock, because it's the most durable and consistent finish, and because we have tons of it. Lots of work to move around. We also use locally gathered stones as filler, and sometimes some local mineral soil where it's easily accessed (usually because we've dug it up while building). You can use a lot more of this, some trails are entirely built with locally "borrowed" material but it's not as long-lived and it's time consuming.
So we build back up to the original level or a little higher (draining again). Interesting features tend to get buried entirely- it's hard to compact stone around a root, frinstance, so we go over it and then compress it with a wacker plate. What's left now is often a 3 foot wide, horrible bmx track.
You're thinking about drainage all the way through btw but that's mostly fairly common sense- does need a fair amount of thought to avoid, frinstance, building a berm that becomes a pond. High and low points etc.
The next stage is internet forums pissing and moaning about how sanitised it is and about how it's a bmx track- ideally based on one photo rather than actually riding it.
The next stage, is riding in. Because we don't generally build the trail how we want it to be, we build it for how it will be. This is why it's hard- people like Andy Wardman at Glentress can do it, most folks can't, I certainly can't, I always think we're ****ing it right up until the day it becomes great.
So, that 3 foot wide tray which is obviously far too wide... Soon, a clear ride line should form. Debris, pine needles, bits of windblown stuff, and eventually vegetation encroach (we do a bit of this ourselves manually to speed it up, when we can). So you end up with, hopefully, a narrow ride line surrounded by hidden armour which protects the main line, reduces damage to the edges (the weakest point) and also helps stop people killing themselves when going too fast.
(nb- in practice this doesn't work as well as you'd hope, because some dicks will ride off the trail even if it's a mile wide if they think it'll save them a strava-second, and because with the sheer volume of riders means that the ride line will be wide anyway)
Next, the trail beds in- there's natural settling and shrinkage as it dries off, some of the fines will blow away, leaving a rubblier surface which is more interesting and natural feeling. Riders will also wear it down, which is good. Those buried roots etc come back to the surface but are still solidly part of the trail, because the rock is so compacted around them, there's no voids.
So all in all... It's almost exactly like building a road, except without the tarmac. It's a kind of insane process but what it gives you is a trail 300000 people a year can ride all year round for, hopefully, a very long time.