Yeah... not particularly hard if you aren't trying to solve literally
all of the engineering challenges that are faced by a mass-production design, as some have noted...

RPM -- is a free parameter. If you go with low RPM, you'll most likely have a motor with many poles, and a very large rotor and stator. Or vice versa at high RPM.
This is a key reason why motors generally spin quite fast, when they can. PMDC, series wound, and BLDC motors*, in handheld scale items, typically hit 5-30kRPM. The torque isn't terribly large, but the core doesn't need to be large either, and a few gears are a lot cheaper (and lighter).
*BLDC is actually a PMAC machine. (PM = Permanent Magnet, AC/DC. BL = BrushLess, meaning, electronically commutated.)
A key design parameter is the Maxwell stress, \$\sigma = \frac{B^2}{2 \mu}\$. When this stress is applied asymmetrically across an air gap, it pushes on the components separated by that air gap. (It has to be asymmetrical, because if it's the same stress at either end of a given unit of space -- as it is for a small segment inside a solid magnetic core, say -- the forces oppose and just compress or stretch the segment, no acceleration.)
The fundamental limit of this (for realistic designs) is the magnetic saturation of steel. Above about 1.2T, the amount of magnetization (ampere-turns per meter) required to cause more flux density (tesla, volt-seconds (flux) per meter squared) starts going way up. The in-circuit consequence is more current drawn on the peaks of an AC waveform (where flux is greatest), and the motive consequence is a limitation of maximum torque.
The stress of ~1.2T is close to a few atmospheres. The power density of an electric motor is coincidentally quite close to that of a regular compressed air tool (which mostly run on say 4-6 atm).
Which is also the limit for a coilgun with a steel armature, a supremely disappointing outcome compared to a potato gun propelled by a tiny squirt of combustible fuel.
Applied to a motor, this pressure shows up as a shear force across the air gap, as the rotor and stator fields try to align. Shear around a cylinder, of course, is just another description of torque, so it makes it rotate.
I'm... assuming you know a bit of classical mechanics to begin with. If not, keep in mind that torque = force * moment arm, so the larger the rotor/stator is, not only is the air gap longer (more perimeter over which to apply that shear force), but the moment arm (rotor radius) is as well. Also, power = force * velocity (or in the cylindrical case, power = torque * angular velocity), which is why a smaller rotor can deliver the same power if it's made to go much, much faster. And, with pressure limited by materials properties and physics, speed is a valuable ally here!
And classical, erm, electrics -- there are in-circuit values (voltage, current, and their ratio, resistance; also, flux is the time integral of voltage, the "area under the curve"), and there are physical values (EMF, flux density, magnetization, MMF..) that start with the in-circuit values, taking geometry into consideration (number of turns, cross-section of the core, air gap length and width..). These are ultimately all simple ratios to each other, which is very convenient: you can always do dimensional analysis to put together a few of these and see what they make.
Tim