Stand a bubble level near the place-of-drillage, and rest the dorsal edge of the drill against the long edge of the level. Ask a friend to hold the level, if necessary.

Align a small section of pipe or straight tubing with an ID that’s just bigger than your bit, and clamp it to the board in some way that keeps it plumb. You could even fasten two other boards to your target board and then clamp the tubing between them.

Then use a long drill bit to drill through the pipe / tube – which is already aligned the way you want – and take care not to drill or rub through the side wall of the tubing.

Many of the newer drills, even cheap ones, have a bubble level on the drill. That would make it easier. You’ll never get it perfect without a drill press but using a square to help align the drill would also work.