Let me put it simple. Gas Laws: When you blow up a balloon, you are adding molecules of gas into it and increasing its volume. Best example of Avogadro's law. Remember only three things temperature, pressure and volume. In hot days, the air in your tyre expands with temperature. Charle's Law- Doubling the temperature of a gas doubles its volume.
When you pump air into a tyre, the gas molecules inside the tyre get compressed and are packed closer (volume decreases and pressure increases) Boyle's law. And yes, P total is always P1 +P2 + P3... Dalton's law. Cooker is heated, the pressure of steam increases...Gay Lussac's law.