How do I convert Cramer's V to Cohen's d? Say I have a chi-squared test that compares 3 different groups:
$\chi^2_2 = 9.81$, $p=.012$, Cramer's $V=.33$
How would I go about converting this to a $d$-statistic? 
Is the proper approach in this case:
$\sqrt{(4\times 9.81)/N}$, with $N$ = number of participants?
 A: There is no general method to convert Cramér's V to Cohen's d.
Both statistics are considered effect size statistics, but they convey different kinds of information.
Cohen's d compares values from a continuous variable between two groups, as might be analyzed with a t-test.  It is essentially the difference in means between two groups divided by the pooled standard deviation.  The absolute value of Cohen's d ranges from 0 to infinity.
Cramér's V is used for contingency tables of counts, for tables larger than 2 x 2.  It expresses how far the counts are from expected values.  It can be thought as the chi-square value normalized for sample size.  It ranges from 0 to 1.
Perhaps certain conditions could be specified where a conversion between Cramér's V and Cohen's d makes sense. For example, where it is known that a continuous variable had a certain distribution and was dichotomized according to a certain rule.  But this would not hold for cases outside of these pre-determined conditions.
A: Cramer's $V$ is an effect size from the 'correlation family' of effect sizes. Therefore, you could convert using the formula for converting $r$ to $d$:
$$\text{Cohen's }d=\frac{2r}{\sqrt{1-r^2}}$$
However, note that this '$d$' is quite different from the regular Cohen's $d$, which represents the difference between two means expressed in standard deviations.
Note
If you're conducting a meta-analysis and the variable that's "trichotomized" in this case, but dichotomized in all other cases, this can be ok if the variable is the same variable (although you'll have to caution when interpretating the result). If the 'trichotomized' variable in reality is continuous, but happens to be operationalized as a categorical variable in this case, I'd suggest instead converting all effect sizes to $r$. Whether these conversions are appropriate at all depends very much on the context and nature of the variables.
