A star is sighted and its position noted with regard to the backdrop of the sky. All that remains to be done is wait while Earth does the work, moving along in its orbit to a point on the other side of the sun. Then, the star is examined again. By then, the baseline distance has grown to some 186,000,000 miles. Now, the star would have appeared to have shifted slightly.
Scientists know the baseline distance, and they can figure the angle of sight.
Then, the complicated math takes over, and using the parallactic figures, the star's distance can be figured reasonably reliably. Other methods of measuring the gigantic distances to stars are in use now, but the early method of parallax is still utilized by scientists as another tool to help them solve the riddles of the universe around us.