Finding $p$ value corresponding to $t$ value, 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 
$p$ value is the probability of finding the observed $t$ value or a more extreme value, given that the null hypothesis is true.
If you have found a positive $t$ value ($t \geq 0$):
If you have found a negative $t$ value ($t < 0$):

Right sided 
$p$ value is the probability of finding the observed $t$ value or a larger value, given that the null hypothesis is true.
If you have found a positive $t$ value ($t \geq 0$):
If you have found a negative $t$ value ($t < 0$):

Left sided 
$p$ value is the probability of finding the observed $t$ value or a smaller value, given that the null hypothesis is true.
If you have found a positive $t$ value ($t \geq 0$):
If you have found a negative $t$ value ($t < 0$):
