You swap weapons by collecting powerups, and as soon as the weapon you want is highlighted, you can press a key (space, if i remember correctly), or quickly waggle the joystick to select it.
If you highlight the same weapon again, and select it, it powers up that weapon. If you select a different weapon, you lose all powerups and start again from the weak version of that new weapon.
The plasma weapon, while not the most powerful to start with, builds up to the most powerful once you powered it up enough.