Construction mode is played with 2 clans (“colors”). The goal is to kill all hedgehogs of the enemy clan. Both clans start at opposing sides of the terrain.

What is special about this mode is that your team is able to spawn certain constructions using the “air attack” weapon. Use the direction keys to switch through the possible constuctions and use the placement key to place it.

The 0.9.21 release news explains the structure types:
http://www.hedgewars.org/node/5897

They are also explained briefly in the [Esc] or pause screen.

Some important rules:
All teams start with some cash or resources or whatever. Each construction comes with a price you have to pay. Weapons and utilities can be bought as well, there are constructions just for that. Your team may always only build on their half of the terrain. You get new resources every round, but you can speed this up by placing some generators. All hedgehogs start with some basic weapons and your ammo is stored on a per-hog basis.
It is allowed to place constructions within terrain.

And that's basically the idea behind Construction Mode, I do not know what else to explain. But I hope it helps.

I certainly have a demo of me versus Wohlstand and also of me versus nemo playtesting Construction Mode. The problem is, I don't know where, my demo collection is huge and most demos only have automatically assigned names. :/
I wish there would be a tool to organize your demo collection. Especially making all the metadata human-readable would be important.

thank wuzzy

i'll watch the server to see if there are some construction to spectate

playing alone was kind of : put generator and play incremental game.... dont know when attack etc...

There is now a more detailed wiki page explaining Construction Mode, including cost charts for better overview:

http://wiki.hedgewars.wohlnet.ru/wiki/Construction_Mode

Note: This is an unoffical fan wiki.