I find that understanding the concept and trying to derive the equations from mental experiments is one good way. A simple example is Pressure. What's the equation for this?
Well I think, if I push harder, apply more force, then the pressure increases.
Now I can either press my hand with my thumb or with a needle, both with the exact same force, but the pressure will be much greater with the needle. So smaller surface area makes higher pressure.
So by these considerations we can recall,
\[P=\frac{F}{A}\]
now if someone says something like, "A man who weighs a mass m is hanging from a suction cup, what's the surface of the suction cup?" what do you do?
Just go for it, write down all the equations you can and draw a picture of the free body diagram. If you're stuck it's better than nothing. Once you see it written out you can more easily recognize what goes together. So for instance,
F=mg is the force of gravity pulling him down
P=F/A has some things in it that we might need, area. So I'm not expecting you to have known this, but I think it's fair to say that air pressure is a constant value so we could look this up just like we looked up the value of g for gravity. Now we can plug one into the other and solve for the surface area A.
Maybe this example is too simplistic but the point is that you can really get a lot of stuff done by just following the units and the equations, they tend to lead the way in some cases. Then once you've reached a point where things don't work out or when you've come to an answer you can check yourself with questions like, "Can an ounce of water hold 1 million joules of heat before evaporating?" Is this realistic or have I gone wrong somewhere?