Q: Statistics Wilcoxon Signed-Rank Test Suppose we measure a change in blood pressure  (after-before) some treatment.
You get a set of numbers that represents this change. 
The question is:
Is there evidence to suggest that the treatment significantly affects blood pressure?
Shouldn't you use a two tailed test here? 
The answer says that I should a one tailed test. 
Would be grateful for any help

A: One or two-sided. Your major issue is one vs. two-sided alternative.
Presumably the subjects have high blood pressure and the treatment
is intended to treat that. Then, of course, one hopes that
the treatment is effective, and might be tempted to use a one-sided
alternative. But if there is a possibility that
the treatment might actually raise blood pressure, then one has
to use a two-sided alternative.
In a real experiment one should use available information to decide
before data are taken whether to use a one- or two-sided alternative.
If one waits until the data are in, then one can see whether the BP
is lower or higher after treatment, and choose the alternative based
on the data. This is a kind of cheating that occurs too often.
It is cheating because the P-value with a two-sided alternative is
larger, and so it is more difficult to reject the null hypothesis (no
difference).
In exercises for statistics texts and courses, one cannot put all of the background
knowledge into the question. So sometimes there is an agreement that
the wording of the question is used to decide between one- and two-sided
alternatives. If the wording is about affecting or changing blood
pressure, it's two-sided. If the wording is about decreasing or improving
then it's one-sided.

For your particular question, I agree with you that the alternative should
  be two-sided. First, because treating blood pressure is notoriously difficult
  and not all attempts produce the results hoped for. Second, because of the
  wording of the question as you state it.

What test to use? Another issue is that you mention a Wilcoxon signed rank test in the title
of your question. This test may be appropriate if this is a paired design
and if it is not clear whether the changes is blood pressure are normal.
It would be a paired design if you had a small number $n$ of subjects
for whom you have a blood-pressure determination before treatment and then
again after treatment, so that we are looking at $n$ before-minus-after
differences (which we hope will be mainly larger than zero). 
We may question whether the population of differences is normal. Blood
pressures can be erratic and we may anticipate some outliers among the
differences. Thus, we may use a one-sample nonparametric test such as the
Wilcoxon signed-rank test. However, if the the 'determinations' were averages of several BP
measurements before and after for each subject, and if the number of subjects is large, it might be
appropriate to use a one-sample t test.
Advanced protocols for human subjects. Because this is an experiment using human subjects, there are ethical issues
to be considered. What are the risks to patients of the treatment and what are the potential benefits? In the US most such studies that rely in part of federal funding (or if approval for marketing a drug is sought) have to be discussed and decided 
in advance. Then the issues of one- vs/ two-sided alternatives and nonparametric
vs t test will be decided in advance of enrolling patients and taking data.
