If you have decided that a one-tailed test is the appropriate test to
use, how do you decide whether it should be a lower-tailed test or an
upper-tailed test?

One needs to know a bit more about the context to answer the Question.

For a symmetric distribution like the normal distribution, there's no
difference in "size" between upper- and lower-tails (for some fixed
distance in standard deviations from the mean).

For an asymmetric distribution like an exponential distribution on
[0,+oo), the most likely scenario for a test of statistical inference
would I think be one using the upper tail, where the probability
density tends to zero.  But I suspect that an experimental hypothesis
could be contrived that would lead to using a lower tail for such a
distribution (i.e. rejecting a null hypothesis based on a small
probability of few observed events in a Poisson process or upon a
dearth of short arrival times).

To say that one has decided to use a one-tailed test suggests that
some conceptual framework exists for dispensing with the more
conservative two-tailed test approach.  The only general observation
that I can think to make is that the rationale for this decision ought
to dictate whether the uppper- or lower-tail of the distribution is
germane to your comparison.

regards, mathtalk-ga