Was everything just left behind or were there organized "clean up" crews covering the trenches with dirt etc. and gathering the remaining equipment?
I reckon it varied depending on the area and country.
To add... Are there any still around today? Saw a recreation of them at the Imperial War Museum five years ago and they didn't seem like they could stand the test of time without some maintenance.
Most people have keyed in that there are trenches and craters left from the battles of WWI, preserved at various locations Ex. Vimmy and Yepres. Here are some of my personal shots from Vimmy:
note the sheep who are the areas lawnmowers due to the massive amount of unexploded ordnance that litter the area. The trenches and tunnels from the battle have been preserved and are there for tourists to experience, you're guided by Canadian volunteers through the tunnels underneath. As for other sights, such as the Somme fields; those have been reclaimed by their land owners for farming and other assorted needs. Every year during the spring thawing ordnance comes up to the surface, in which the French government goes around with special teams to clear those hazards.
It depends on where the trenches were. On land that was previously used for farming such as on the Somme and Arras battlefields, the trenches and craters were filled in and the land reverted back to grazing or crops. In other areas where the land is less useful such as wooded areas the trenches and shell holes were simply left to erode naturally, not worth the effort of filling in.
Some trench systems have been preserved as have heavily shelled areas simply because they are too dangerous to use, the most notable being the Vimy Ridge battlefield. There are other reasons of course, preservation for memorial reasons such as the Newfoundland Memorial Park where 1916 trenches are still present.
If you can get hold of it, there is a wonderful old three volume series called: "Twenty Years After-The Battle Fields of 1914-18:Then and Now" Edited by Maj.Gen. Sir Ernest Swinton K.B.E, C.B. which gave comparative photos of the battlefields at the time and then in the thirties.
As others have noted, urban reconstruction was the fastest although some small hamlets were just abandoned. Farm land was ploughed, but someone must have done some serious work removing munitions. In some places the fields have just been left as the craters were too big or too many munitions (some are still found today).
Many forests were left for ages as clearing was much more complicated (some becoming memorials).