What is the use of a 2-tailed test? If T > critical value in a 2-tailed test, what is the next step we should do? I don't really see much use of the negative tail side.

If your alternative hypothesis is HA: µ ⌿ k (for a certain k), then you should reject H0 when T is either too large (say >c) or too small (say <-c). Such test is called two-tailed as one can reject H0 when T is either < -c (the negative side) or > c (the positive side). Moreover, you may observe that when the test is significant, the conclusion can either µ < k or µ> k, depending on whether the sample mean is < k or > k or T is < -c or > c. A two-tailed test enables us to make either conclusion.