Confidence interval equation
CI = effect size +/- (appropriate multiplier x standard error of the difference)
Appropriate multiplier = (alpha level / tails) x critical value
The alpha level is the probability, the researcher is willing to accept, that the findings are a result of sampling error. It is determined by the level of confidence the researcher decides to use, and is typically set to either 90%, 95% or 99%. The greater the confidence level, the wider the interval. Sample size can also affect the width of the interval, with smaller sample sizes leading to wider intervals. A confidence of 95% will provide an alpha level of 0.05.
The number of tails depends on the question the researcher is asking. Two tails are used if the researcher would like to know if the results of an intervention differ from a control or alternate group. It is common to use 2 tails in intervention based research.
Link: t-distribution table
The pooled SD is the weighted average of each group's standard deviation. It should be used when comparing the mean difference between two different (independent) groups.