The controls consist of just a joystick and one button (fire). You are a floating, jet-packed, astro-dude who can fire either left of right (always the direction you are facing). Your jet-pack helps you float a little... You can push up on the joystick and you will fly up, and then if you let go, you kind of float downward. Pull the joystick down to go down more quickly. Push left to face left and then head off that way. Push right to switch back to facing right and then fly off that way.
The initial premise is that a volcano is spewing hot stones that turn into fireballs. You have to shoot them all to end the first couple of levels. Meanwhile, there are also dragons flying around to shoot. If the dragons eat the fireballs they can breathe fire at you (give them a mint). You can shoot or avoid the dragons, because the goal of the round is to shoot all the rocks/fireballs - not the dragons - and the round ends whether you've killed the dragons or not. Of course shooting them scores points and gets them off your ass.
The game vaguely looks like a distant cousin to Joust. Of course it doesn't approach the classic gameplay or look of one of my favorite games of all-time (Joust), but it's a fun game in its own right and does have some things in common with Joust. First, if you take too long, there are some screeches and a more aggressive dragon comes out (just like the pterodactyl in Joust). Second, the playfield is kind of set up with floating barriers and obstacles in the vein of Joust - although you can fly through them in LizWiz, unlike in Joust.
In subsequent rounds, you have to rescue humans. They are floating around in bubbles and you rescue them by picking them up and dropping them on the landing pads that appear at the bottom of the screen. It's important to note that you can only rescue/carry one at a time. Also like Joust, there is an early stage where there are bubbled humans everywhere (kinda like the egg wave in Joust).
Later (stage 4 or 5??), there is a spider-type wave. A completely diff kind of round where a group of them come down hanging by a thread and you have to shoot them before any one of them reach the bottom of the screen. It's a completely diff kind of round than the previous one that adds to the gameplay.
The controls can be a little difficult to master and you run into the problem that occurs often in these type of games... since you only shoot the direction you are facing, it's hard to run away from stuff and still fire at it. Conversely, you have to be careful that when you turn to fire at something, you don't fly right into it.
Lizard Wizard wins lots of points for uniqueness and originality (despite some similarities to Joust), crank it up and slay a few dragons.