Engineering overview

You are the Station Engineer, everything that breaks is supposed to be fixed by you. You get a lot of useful tools to fix various things on the station. A good engineer responds to emergencies promptly and repairs things fast so the rest of the crew can go on with their life.

Tools and equipment

You spawn with a full toolbelt. Almost everything can be manipulated with one of these tools. If you are in doubt what to use, try the crowbar!
Insulated gloves are a must have to avoid electric shocks. There are a couple scattered around in Engineering and more in the electrical supplies locker. Cargo can order more. Working without these can be harmful or even fatal!
A Multitool is useful to manipulate wires of every kind. You also find this in the electrical supplies locker.
A Welding mask is essential for welding if you want to keep your eyesight. You find these in the welding supplies locker. Also grab an Industrial welding tool and replace the one in your belt with that.
The maintenance tunnels are dark. A good engineer always has a Flashlight on him.
You also need a Meson scanner. Never look into the singularity without these! It also makes you able to see hull breaches through walls. Scientists can hook you up with an advanced version that doesn't require lights to work. Available from the engineer's locker or the YouTool vending machine.
Hazard vest. This doesn't do much but you can put your oxygen tank in it's storage slot so you can use your other slots for tools. Get it from racks or from engineer's locker.
Engineering hardsuit. This is a must have if you plan to go into space for some reason. Since there is only two of these provided in the suit storage units, make sure to only take them if you really need them. Walking around in a hardsuit just in case is considered powergaming and also annoys other engineers who might actually need the suit. The hardsuits provide decent but not total protection from radiation.
Radiation suit. Available from the radiation suit closets. You need this if you have to work near a Radiation collector array or the Particle accelerator while the singularity is active.

Materials and components

Metal is the most commonly needed material. You can build every kind of things out of it. You can find metal in Engineering storage, Engineering secure storage, EVA and Auxiliary Tool Storage. Cargo can get you more if you run out. Metal can be turned into metal rods, another commonly needed material.
Glass is mostly needed to make windows. Can be found at the same areas as metal.
Plasteel is mostly needed to build or repair reinforced walls. Not much is available on the station so only take it if you need it.
Cable coil is required to lay power wires and to build most electronic equipment. You have one coil in your toolbelt and you can get more from the YouTool in engineering. Also a lot of these are scattered around the station.
A power control module is needed to build or repair APCs on the station. It is handy to have one on you.
Airlock electronics is an essential component in Airlocks which often get broke and need a replacement. You can set required access level by clicking it in your hand and swiping it with your ID.
Air alarm electronics is rarely needed but should you need it, they are available from the Engi-Vend in engineering.
Power cells power a couple of equipment on the station. Having one on yourself is handy.
You are sometimes required to build new Computers or Machines. Components for these can be found in Tech storage.

Your usual shift

When the shift starts, the first responsibility of the engineers is to start the singularity. This can be easily done by completing each of the steps below:

Assemble the Particle accelerator in the center of the engine room by wrenching, wiring and screwing all parts of it.
Put a Plasma tank into each of the Radiation Collector Arrays. Optionally you can fill the tanks from the canister in secure storage so the engine provides more power. If you opt for this, be very careful to not let the plasma leak.
Grab a hardsuit and walk out into space south of the engine room. Turn on all the four Emitters and lock them by swiping your ID. Also go around and turn on each of the Field generators. If it's late to the shift the emitters might be unpowered preventing you from setting a containment field. Please check the Detailed guide to starting the singularity.
Head back in, dress in a radiation suit then use the console on the Particle Accelerator. Turn it on and set it to power 2. Observe the singularity growing, wear a meson scanner to avoid unpleasant side effects. Once the singularity is 2x2 in size, notch the power level back to 0. Leave it ON.
Exit the accelerator room and close the shutters.
Finally, go into the SMES room and set each of the SMES units. If you filled the plasma tanks in step 2, set them to input level 200000, if you did not, set them to input level 120000. Set output to 100000. Make sure both input and output is turned on.
From time to time, check that all is well with the engine. Malicious people or silicons might have messed with it, which can result in a disaster. Make sure the containment field is up and that accelerator and SMES units are on the correct settings.

Setting the solar arrays:

Four solar arrays are on the station which can also provide power to the station. Grab a hardsuit and a couple of cables to set them up.
Complete the wiring on the array of your choice.
Head back in and set the solar control computer to Auto tracking.
Set the SMES unit to input level 70000 and input on. If you have the engine running, set output to off. Otherwise, set output level to 50000.
Repeat until all arrays are operational.

Fixing hull breaches:

Grab a hardsuit and head to the scene.
First, replace all missing plating (use metal rods on space to build a lattice and floor tiles to build plating on a lattice) and walls facing space (click metal to build a girder and use metal on girder to finish wall).
Use a welder to repair broken plating.
Lay all missing wires, your priority is to restore power flow to other areas of the station if the wires leading to there are destroyed. Fix/rebuild broken APCs.
Fix/rebuild essential equipment that was destroyed (computers, machines).
Repair internal walls and windows. Atmos technicians must have arrived by now, consult with them to not block their piping operations with things you build.
Lay floor tiles on plating to make it look nice again. Rebuild destroyed furniture.