For making an edge straight, you can stretch a thread with a bow- like the bow of a bow and arrow. If you put ink on it and snap it against a piece of wood, it will mark a straight line ( and carpenters' chalk lines still work on this principle). Saw or cut to that line, and you have a straight edge. ( If you want a smooth straight edge, it's a bit more complex- you need two straight edges and something like soot or colored grease to rub on them: this can tell you what high spots need to be shaved off, as you rub one against the other and scrape until they are both evenly colored. Check with the stretched line to make sure you're not making one concave to the other's convex).

To make a square, once you have the straight stick for a base, you fasten another straight stick sort of perpendicular to it- drive a nail into it, so it can still stiffly pivot a little. Scribe a line along the base stick and the perpendicular stick- it will make a sort of right angle. Flip the square over and scribe the lines from the same point again. However much the stick is off of perpendicular, that error is doubled between the two scribed lines. Keep adjusting the perpendicular stick until the same line is being scribed. Then put another nail into the sticks, so they won't move , or brace them with another stick nailed across the ends, to make an even more solid triangle. If you do this and play around a bit with the same technique of scribing and flipping, once your have a reliable 90 degrees square you can also set that brace stick to make an isoceles triangle, which will also give you 45 degrees for marking miter joints.

This may sound like something for the ancient Greeks, but this method of scribing and flipping the square is the one still often used to check carpenter's framing squares after they've been knocked around a bit.