If you look at a product or division, the way is to start with one thing.
Look at 'Newton-second'. This means a newton applied for a second. A newton is a force, a shove, so to speak. You shove something for a second, and it starts moving. If it weighs a kilogram, the effect of a newton-second is to make it run at 1 m/s. If it weighs 10 kg, it will run at 1 dm/s.
A metre-newton of torque, is where you pull on a handle with newtons of force, at a distance of metres. The old rusty nut isn't going to turn too fast unless you get a longer spanner. Then you need to pull more to get the same angle, but it's a bigger force.
If you get something like 'volts per metre', it's a gradient. 'per metre' often gives gradients, or weights of wire. So volts per metre here is a gradient. The unit translates to newtons per coulomb, and it's the electric force doing the shoving. Here the size of the handle is in coulombs, and the newtons come as force.
Sometimes it's better to look at how the quantity is defined, and then see if you can make the units to work. One quantity i came across was 's/m' of permeability. It works like this. The actual thing is 'flow of liquid per area, divided by the driving pressure', so (kg / m² s) / Pa. But when you put Pa = kg / m s², the division gives s/m.
Another unit is 'W/m K'. This is thermal conductivity, or energy flux per driving temperature gradient. What it means is (energy / area / time ) ÷ (temperature / thickness). The fps unit is Btu / ft² h ÷ °F / in, or the unit Btu in / ft² hr °F. Replacing these with their metrics, gives J.m/m² s K, or W/m K.