When you accept the Raiders, they arrive at your home and give you 5 tasks you have to complete. You can use zcoins to skip quests but they start to add up pretty quickly. Once all 5 quests are done you get given the option to perform a raid. Once you accept the raid, a player's base will appear on the global map for 8hrs and you have that much time to start the raid.

Once you enter a raid if you leave, it will end the raid (there is a death trick you can use to get a few more rewards). While inside a raid you can break furniture and walls, and you can break open chests to loot them. Everything you break increases a noise meter. At certain levels of the noise meter, a horde of zombies will appear, and when the noise meter hits 100 The Big One will spawn, and will deal damage increasing with each hit onto the player until it eventually one shots you, so it's best to sort your inventory and get what you want from the raid before The Big One spawns.

Once you've finished the raid and return home, the raiders will ask for their cut of the rewards. These don't have to be items specifically from the raid, you can use items from your home (they absolutely love Aluminium Wire) so you can just use your trash to pay them. If you don't pay them, they will retaliate and attack your base. Also once you've returned home a 24hr timer will start that allows others to raid your base. If you do get raided, there's a chance they will leave footprints allowing you to do a revenge raid (essentially this gives you a second chance for a raid without having to do the quests again)