Q:

In a force model, $F = ma$, how to understand the units?

For instance, in an aerodynamic force model, the force terms can be lift terms, drag terms, both of which have translational velocities as factors in their models; but, velocities are in units of, say, meters/sec.  
Meanwhile, there are gravity force terms to add in to the model, but the gravitational acceleration, g, is in units of meters/seconds-squared.
So, how do we resolve this apparent issue of adding force terms with different units?

A:

So, how do we resolve this apparent issue of adding force terms with different units?

They do not have different units.
Put all the units of each side down :
A force is in Newtons ($N$) and you already now what mass and acceleration are in.
$$Force = mass \times acceleration$$
gives us :
$$N = kg\,m\,s^{-2}$$
Which is exactly what it should be because that's what a Newton's units are.
All forces will work out that way and if they don't you have either gotten the units of something wrong or done the maths wrong (a useful check).

For instance, in an aerodynamic force model, the force terms can be lift terms, drag terms, both of which have translational velocities as factors in their models; but, velocities are in units of, say, meters/sec. 

Forces like this will have some constant term which has the right units to balance everything out.
Sometimes aerodynamic drag is modeled as :
$$F = kv^2$$
The units of $k$ will be what is needed to give a unit of force to both sides.

