if there ever was a race that needs flowcharts it's this one
There's a tinkering flowchart in the manual, at the bottom of the Items section.
In general though:
metal sheet (forge, under 'other items') -> 10 metal strips (tinkerer) -> simple mechanical parts (tinkerer) -> complex mechanical parts (tinkerer)
complex mechanical parts + gear armor items (forge) -> special armor items (gadgeteer)
complex mechanical parts + automaton frames (forge, under 'other items') -> automatons (clockwork automaton workshop/automaton body shop)
To get magnets:
glass tubes (glassmaker) + foil (tinkerer) -> capacitor (tinkerer)
capacitor -> charged capacitor (electrostatic generator, requires power)
charged capacitor + electromagnet (tinkerer) + iron, nickel, or cobalt bar -> magnetized metal bar (smelter)
Magnetized metal bars can be used for dynamos, railgun ammo, or broken down into small magnets to create more complex machines.
Or if you're lazy, you can buy most of the important items in crates (an oscilloscope is included in the 'crate of geological analysis tools', a dynamo is included in the 'crate of heavy electrical equipment', a 'crate of automaton parts' contains everything you need to make one automaton aside from the actual frame, a 'crate of assorted mechanical parts' includes several random tinkering items, and a 'crate of technological wonders' contains random ready-to-use mechanical armor or weapons). This is more expensive than making them yourself, though.