To start with engineering, you simply burn twigs and collect the ashes. The ashes will come in handy later on.

After you get up to a certain level, you can get the rope making book and start making ropes. You can even do this in the cotton field where you make the thread. Later, nails and caltrops can be made.

The best way to get going in this skill (it is expensive the farther in you go) is to make a ton of ashes and then when you have the book, start making ropes.

Ashes will be used at higher levels for mines, and ropes will be used for astro indicators.

Snares and Caltrops are both pretty worthless.

When you are around level 10 start making nails and saltpetre.
Around level 15 start making blackpowder.
Nails, saltpetre, and blackpowder all take more work than ropes and ashes, and you won't use them until you are at higher levels, but they are nice to make for a change of pace.

When you are around level 20 is where the fun begins. Start making poison caltrops, then work into indicators (this is where you'll use your ropes).

Around level 25 you can start making arrowheads. You'll work into arrows a few levels later.

After hitting the mid 30's you can start working on landmines and more complex arrows/bolts.