Yes, I'm trying to figure out how to play eradicate as well
You have four actions per turn, represented by the number of bullets at the top of the screen. Actions you can take are: move to an adjacent connected city, defeat a zombie horde in your current city, fly to a city resource in your "hand", build an airport in your current city, fly to an airport, trade resources, and stabilize a region.
To move or fly you use the airport icon beneath your character (symbolized by a number of dots for first, second, third, and fourth players). Flying to a city in your hand requires you to discard that resource. Flying to an airport requires that you fly from a city that already has an airport.
To defeat one zombie horde in your current city you use the red battle icon beneath your character. There can be up to three zombie hordes in a city at a time. If a fourth one is to be added the outbreak counter goes up one, and one zombie horde is instead added to all connected cities. Once a region is stabilized, using the defeat zombie horde action clears the city completely.
To build an airport in the current city you use the orange airport symbol beneath your character. Building an airport also requires you to discard the resource of the current city. Airports are important because you need them to stabilize regions.
To trade resources with another player, you need to both be in the same city as the resource to be traded. The action will allow transfer of that city resource from you to him, or him to you.
To stabilize a region, you need to have five city resources from the same region, and be in a city containing an airport (you do not have to be in a city of the same region you are stabilizing). If after stabilizing a region, you remove all zombies from that region, that region is considered eradicated. The equivalent to this in pandemic is not something I advise to do normally, but since eradicate is point based and you never really lose, just score less/more, I'd say it's worth pursuing unless it prevents you from stabilizing another region or ending the game via game turns.
There are also white resource events that are pretty much free actions, in that they do not take up one of the four actions you have per turn to use. You can also use them outside of your turn.
Garrison-garrison a city remotely, removing all zombies in that city and prevent new zombies from invading.
Interdict-reduce the zombie encounter to zero for one turn.
???-airlift a player to any other city
???-build an airport in any city
???-active player can take two more actions
There are probably more but I can't think of them right now.
The game phases per turn are as follows:
Take four actions
Draw two resources
Zombies invade
The resource drawn can be either a) a city resource b) a special event resource or c) a zombie outbreak
When a zombie outbreak occurs, all previous invaded cities are susceptible to invasion again (the invasion discard pile is shuffled and placed in top of the invasion draw deck) additionally, a new city is drawn and invaded with three zombie hordes.
....stopping here because astrolad is smarter than me and posted the pandemic rules pdf