I'm a Mechanical Engineering student, :P but I'll try my best to explain.......
How much work is done on a computer is greatly depending on the job title of Engineer.
Engineering Technicians (TechEng) are more likely to be working with hands since they're "Technicians".
Chartered/Incorporated Engineers will also be working with hands (but only a little), they're specialized on the theory side of the Engineering, such as CAD, etc.
A proper Engineer will work with hands as well as by computers.
They'll typically need a:
Computer
Computer controlled manufactoring machines (Computer Integrated Manufactoring, CIM)
Pens and paper
A deadline plan (could be a project manager too)
Everything has to be planned out, theory comes first (not always, but mostly).
An Mechanical Engineer will use AutoCAD and Mechanical AutoCAD, while a Civil Engineer will also use AutoCAD with AutoCAD Civil software.
Using a CAD software is very complicated, definitely not for someone with very little Engineering knowledge but for someone, who wants to virtualize real time Engineering.
e.g. "Computers may be used to virtualize Engineering concepts"
How much time it takes to do it on CAD, it really depends on the project that the Engineers are working on.
As far as the "CAE" that is mostly related to Mechanical Engineer, but then again, there are numerious of metal parts in Civil Engineering. I don't know what CAE software do Engineers use, but Google it.....
Wikipedia
"Instructions for manufacturing a part must be fed to the necessary machinery, either manually, through programmed instructions, or through the use of a
computer-aided manufacturing (CAM) or combined CAD/CAM program. Optionally, an engineer may also manually manufacture a part using the technical drawings, but this is becoming an increasing rarity, with the advent of
computer numerically controlled (CNC) manufacturing. Engineers primarily manually manufacture parts in the areas of applied
spray coatings, finishes, and other processes that cannot economically or practically be done by a machine."
This is useful on Civil and Mechanical Engineering. Some Civil Engineering companies may produce some metal parts to be used in construction......