Finding critical value $t^*$ given significance level $\alpha$, using the table with critical $t$ values
Assuming a table with a row per degrees of freedom and a column per upper tail probability
Two sided 
Reject the null hypothesis if the observed $t$ falls in one of the two most extreme $\alpha$ / 2 areas of the $t$ distribution. In order to find the critical values $t^*$ and $t^*$ that correspond to these tail areas:

Right sided 
Reject the null hypothesis if the observed $t$ falls in the highest $\alpha$ area of the $t$ distribution. In order to find the critical value $t^*$ that corresponds to this upper tail area:

Left sided 
Reject the null hypothesis if the observed $t$ falls in the lowest $\alpha$ area of the $t$ distribution. In order to find the critical value $t^*$ that corresponds to this lower tail area:
