Most poster boards are let down by the mounting rather than the content. Bubbles and lifting corners read as carelessness from across a room.
Dry beats wet
Water-based glue expands paper, and the paper then dries at a different rate to the board underneath. That mismatch is what causes rippling. Double-sided tape, glue dots or a dry adhesive sheet avoid it entirely. If you must use a wet adhesive, apply it thinly to the board rather than generously to the paper.
Work from the middle out
Tack the centre of the sheet down first, then smooth outwards with the flat of your hand or a soft cloth. Air has somewhere to go that way. Starting at a corner traps a pocket you can never quite chase out.
Give edges something to hold
Corners lift because they are the least supported part of the sheet. A small square of tape under each corner, placed before the main adhesive, stops the problem before it starts. Leaving a consistent margin of board visible around each element also makes the layout look deliberate.
Before you print
Decide the margins first and print to fit them. Trimming a printed sheet to size after the fact almost always ends with one edge slightly out of square, and that is visible once several elements sit side by side.