The 't' test is better known as the ' Student's t test'.
"A student" was the publication psuedonym of R.A. Fisher.

t= |(error in Mean Value)|/(Standard Error of mean).

The divisor is the standard deviation divided by the square root of the the
number of measures. The dividend is simply the positive difference of the
population mean and the sample mean. So you measure the standard error of
mean and to calcualate 't', use the knowledge of the actual mean for the
universe of possible events.

The 't' value so calculated is then used to find a locus between two
adjacent curves of probability significance of a logarithmic plot of the
caculated t value against the logarithmic plot of the number of degrees of
freedom.
These curves of significance level is known as the 'Student's t
distribution' for levels of confidence (from near-zero to near certainty).
See a statistics text for the equations of the distribution, which are quite
complex. I can offer a look-up table of factors and a simple equation to
generate a very close approximation. Conf=f((t,n))

So for two samples you can now compare their t-values and their confidence
levels.
From this you can now calculate the probability that the two samples belong
to the same population.