You can build trenches freely wherever you please with use of engineering trucks, simply select a engineering truck, click the build button (Z) and click dig trench (E), then simply right click where you want it and move the mouse to make your trench as long as you like and what kind of direction you want it to go and right click to make it start building. The buttons are located in lower left corner, and you can hover over them with the cursor to see what it dose. You can also build anti-tank obstacles, barbwire, anti-tank mines and other cool stuff. This all can be built on any mission or map as long as you got a engineering truck. (the truck that repairs tanks and such.)

And you got a infinitive amount of resources in you have or capture a supply depot, but all units have limited supply of ammunition and supplies, and must be restocked from time to time. Supply trucks burn supplies by giving out ammo to your friendly troops while Engineering trucks burn supplies by repairing friendly tanks, building bridges, and placing mines and anti-tank obstacles and barbwire. You can select a supply/engineering truck that is out of supplies to restock by right clicking on a supply depot. (It looks like a bunch of creates stacked together, while your base one is a hangar/garage looking building, they also have a house icon above in ether green or red to indicate who currently control it.) Lower left shows a bar of how much supplies they have left, so if you pan to build a bridge or such, its important that the engineering truck is practically maxed on supplies, as it will cost about 80% of its supplies to build a wooden bridge for you.

Just remember you can only build bridges on specific spots of the map that have a transparent bridge indicating you can build a bridge to cross it. A word of warning, Wooden bridges can break from heavy weight, so if you try drive a Matilda tank across it, it will probably collapse due to how heavy it is, thus killing/destroying your unit in the process as it falls into the river. This also applies to enemy tanks, so use this to your advantage.

And a fun note, its possible to destroy bridges by shooting at it with artillery or such, but if you plan to deny the enemy the ability to cross it, a neat trick is to use a engineering truck and place mines on the bridge, making the enemy tanks lose their threads trying to cross it, thus blocking the whole column of enemy forces form crossing the bridge. as you ponder them to gravel. But if your tanks and heavy guns are unable to deal with their thick armor, simply destroy the whole bridge by bombarding it, causing all enemy units on-top of it to fall to their death. And once they are all dead, you can proceed with simply repairing the bridge with engineering trucks. (But may take a few turns tot he supply depot, as rock/concrete bridges costs a lot of resources.)

This all should work in both multiplayer and singleplayer. (But may be harder to pull off due to how the enemy players probably wont give you to much time to set up, but you should be able to dig quite a few trenches pretty fast.)

Assault mode maps work best for this, as the defender got plenty of gear and time to prepare for the incoming enemy assault.