This video steps you through programming the invT function into your Ti 83/83+ calculator. The invT function is similar to the invNorm function; it computes tvalues given two inputs: the area to the left of the tvalue you are looking for, and the degrees of the freedom. In other words, it is the inverse of the tcdf function.
Update: As someone very helpfully suggested, use the "ALOCK" (alpha lock) when typing in alpha characters so you don't have to keep hitting "ALPHA" before each character.
I would like to express my thanks to Prof. Brian Stonelake of Southern Oregon U for providing the captioning for this video.