the event you have to be ambushed into
Martian Madness has no summoning item. It begins when a Martian Probe spots you and then gets away. The probe drifts around the outer thirds of the map, most often up in the space layer, and its lights turn red the instant it registers a player. From that moment it flies for the edge of the screen, and if it leaves view intact the invasion starts.
Shooting at it does not count as detection, which is the part that catches people. You have to let it see you and then let it go. Minions are the usual reason an attempt fails, since contact-damage summons will chase and kill a probe before it escapes. Dismiss them while you are hunting one.
making a probe appear
Probes only spawn in the outer thirds of the world, so a base at the center will never produce one. Build a platform out toward a map edge, climb into space and wait. A Water Candle works up there and is the difference between a five minute wait and a forty minute one, which matters after your first clear because the probe spawn rate drops sharply.
Nothing will spawn while the Lunar Events are running, while a Martian Madness is already in progress, or while another probe still exists somewhere in the world. Exiting the world just before a probe despawns will also cancel the whole thing.
it starts on top of you
Every other invasion enters at a world border and takes up to about a minute to arrive. This one begins at the world spawn point immediately, so there is no grace period in which to finish an arena. The usual range rules still hold: you need to be within roughly 187 tiles horizontally of spawn and no deeper than about 67 tiles below the surface, or else stand near a town NPC and accept that only about two thirds of spawns will be martians.
the kill count and the saucer
Clearing it takes 200 kills solo, with forty more for every extra player above the 200 health line. Most enemies are worth one. Tesla Turrets are worth nothing at all, and the Martian Saucer is worth ten.
That last number is the entire strategy. The saucer carries the loot people run this event for, and it cannot appear until the invasion is 30 percent complete, becoming common past 50 percent. Kill efficiently and you will finish before many saucers have shown up. The counter is to stop progressing on purpose. Two Teleporters set about 500 tiles apart let you flick away from the infantry so they despawn instead of dying, and the Magic Conch does the same job for free by dropping you at the ocean. The counter stalls, the saucer rolls keep coming.
fighting the ground roster
The infantry is a wall of ranged chip damage rather than a set of individual threats. Ray Gunners and Gigazappers fire on sight, Brain Scramblers throw a confusion effect that will walk you into something worse, Martian Walkers shell you from across the arena and Martian Officers put a shield up that soaks projectiles until it is broken. Scutlix beasts charge in a straight line and are mostly a nuisance.
Saucers fight differently. They hover out of melee range, sweep the arena with beams and rockets, and take genuine damage before they drop. Meet them in the open with room to move sideways, because anything you build for cover will be dismantled underneath you.
what you get
The saucer's table is the reason the event sits where it does in progression: the Xenopopper, Influx Waver, Laser Machinegun, Charged Blaster Cannon, Electrosphere Launcher, Xeno Staff, Cosmic Car Key and the Anti-Gravity Hook. Several of those hold up all the way to the moon lord.
Expert mode does not improve any of those odds, unusually, so there is no reason to raise the difficulty purely for a farm. Clearing the event once also unlocks Martian Dye trades at the Dye Trader and a few paintings at the Traveling Merchant.

