You can make the building process a lot easier by taking your time at the lumberyard. Pick through the stacks to find straight, flat stock. If you choose plywood, it’s a good idea to stick with Baltic birch, which is free of voids.
You’ll never get a good fit with out-of-square or twisted parts. Since a drawer needs to be not only square but also flat to slide properly, one bad piece can ruin the whole drawer. Don’t fool yourself into thinking a piece will straighten out when it’s clamped up. Taking the time to joint the workpieces flat on one face and then planing them to a uniform thickness is the first step in successful drawer construction