For example, if you are looking for z_alpha/2 in order to make a 95% confidence interval, then your confidence level is .95, and your alpha is .05 (if you're 95% sure, you are 5% unsure). Then you should plug into your TI-83 calculator either:
invNorm(1-.05/2)
OR
invNorm(1-(1-.95)/2)
Either way, your calculator should give you 1.96

T Table