I have a guildmate who is about to begin his career as an engineer so I thought I would make a quick guide for it.
The first step in engineering is actually to learn mining. Ask a guard where to find a mining trainer and pay him a visit to learn the trade. If it's available you also need to learn the Smelt Copper skill. Make sure to buy a pickaxe from the mining supplier or you won't be able to mine. Keep this axe in your bags at all times. You will want to keep a good sized bag empty at all times to store your rocks and metals. Before you do anything, go into your spellbook under the general tab and set shortcuts for the Find Minerals skill and the Smelting skill. Use the find minerals skill and you will see a little icon appear by your radar. This will show you mineral deposits on the minimap. Make sure this is always on.
Then go to the engineering trainer and learn the engineering skill. You don't need any extra tools because you will make them yourself. Also be sure to pick up any other skills he can teach you. Whenever you're around a major city, be sure to stop in and meet up with the engineers to train and learn new skills. Go to the general tab in your spellbook and set the Engineering skill to a place you can find it. Then you're good to go.
Now it's time to gather some materials. Check out the mining section to see my tips on finding ore. Make sure your ore tracking is on. If you're a hunter or other class that uses tracking, you will have to keep switching ore finding on so you will see when minerals are near. Go to an area with a lot of copper and start collecting it. You will find copper ore, rough stone, and rarely malachite, tigerseye, and shadowgems. These will be your basic materials for engineering. Engineering often uses other materials like cloth and leather, along with other random items.
Once you have a couple stacks (20 or so) of materials, head back to town and find a forge and anvil. Pull up the smelting skill and click on smelt copper. Then hit the smelt all button to turn the ore into copper bars.
When you have smelted your ore, Now You can also turn rough stone into blasting powder. Be sure to make the easiest item first. You will notice that just like your quests, the skills are colored. Each time you make an item, your skill will increase. Orange items will definitely give you a skill point each time you make that item. Yellow items will most likely give you a skill point each item, or once every 2 items. Green items will give you a skill once every 2-5 items, or sometimes even less frequently. You want to target the orange to yellow skill levels as much as you can.
The first thing you want to do is use up all the rough stone you can to make blasting powder. This is the easiest skill to make and it will turn green soonest. There is no other use for rough stone in engineering so use up all the stones you can. You will later use this for explosives. When your stones are gone, use your copper bars for copper bolts until it turns green. Then move on to crafted light shot and so on.
When you make an arclight spanner, keep it in your bags if there's room or in the bank if you do most of your engineering in a major city. This tool will be needed for construction later on.
Each time your skill goes up by 5 or 10, you will probably have another item you can craft available from your engineering trainer. As your skill goes up you will need more and more unique and hard to find items. Save up your cloth, jewels, and leather in the bank for use later on.
You will see a bar for your engineering skill level at the top of the engineering panel. This will fill up as you level up. When it gets close to the top, make sure to seek out the next level of engineering trainer. For example I believe you can train for the second skill level at 50 skill. If I remember correctly, you can get a maximum of 75 skill at that level. At 75, the skill bar will be full and you won't get any more skill. You can't get past 75 points until you train for the next level of engineering which will allow you to get up to 150 skill.
Just keep making items that are easy to make and useful to you. Have fun and keep up the good work. I'll post more guides on this when I can.