you need to assume that the two samples are coming from normal populations.

Next we can either do this assuming the two population variances are equal

or that they are unequal, see...

Unequal sample sizes, unequal variance at Student's t-test - Wikipedia, the free encyclopedia

vs.

IF we assume equal variances the test stat is

that has a t distribution with degrees of freedom.

(We can do a test to see if the pop variances are equal.)

If they are unequal, you need to do satterwaithe's approximation.