How long would a near-light-speed trip to proxima centauri take from the traveler's and the earth-observer's perspectives? Lets say the spaceship is traveling at .9c to Proxima Centauri. How long does this trip take from the observational standpoint of the passenger vs. the observer from Earth?
Proxima Centauri is about 4.25 light years away.

4.25 / 0.9 = 4.72 years, for the observer on earth. See fourth grade math for info on the calculation.

For the person on the ship, he is undergoing time dilation of about 2.29, which results in 4.72 / 2.29 = 2.06 years. See for example https://www.fourmilab.ch/cship/timedial.html for info the calculation of the dilation.