What do you mean by star positions? Like, in the sky so that you know where a star will be so you can see it with your telescope? Because yeah, stars can be predicted. The positions of stars in the sky change over the course of a day because of the rotation of the Earth, so there are two numbers we use to locate a star in the sky. Declination and right ascension.
Imagine, if you will, a big sphere around the Earth, this is called the celestial sphere. Everything in the sky is found on the celestial sphere, it's exactly like a planetarium, except it goes all the way around the planet. The equator lines up with the celestial equator and the same goes with the celestial north pole and south pole.
Basically, declination is the same thing as latitude and right ascension is similar to longitude. Declination is easy, because the Earth only rotates in one direction. A position in right ascension changes as the day goes by. They are measured in hours, seconds and minutes. 24 hours around the whole thing. So what you do is you take your current local time, compare it to the right ascension, and then subtract some number of hours from the right ascension value, and there's the current spot. Then you line up your telescope and find the star.
It's a lot more complicated than I made it sound, but that's the gist of the idea.
Over the course of tens of thousands of years, the axis of the Earth's rotation moves a bit due to a thing called precession. Basically, the north star will change over time. I think it takes 27000 years to do a whole rotation.
Then of course there is the movement through the galaxy, but that takes tens of millions of years.