Q: How do i play a mission downloaded from A3M?
Copy the downloaded PBO file to one of Arma 3 directories depending on whether this is a Singleplayer or Multiplayer scenario. If you downloaded a ZIP archive (for example from ModsFire), copy the PBO file inside, not the archive.
Singleplayer scenarios should be copied to Missions folder in directory e.g. C:\Program Files (x86)\Steam\steamapps\common\Arma 3\Missions.
Multiplayer scenarios should be copied to MPMissions folder in directory e.g. C:\Program Files (x86)\Steam\steamapps\common\Arma 3\MPMissions.
Campaigns are technically mods (a folder with multiple PBOs), can be stored anywhere and loaded as a local mod in Arma 3 Launcher.
Scenarios, unlike campaigns, will not appear in your Launcher and will be accessible either in Singleplayer->Scenarios menu or Multiplayer->Host menu appropriately.
Always remember to load required dependencies, both mods and DLCs if listed, do that manually or by importing an HTML preset.
Q: Where do I put a scenario playable both SP and MP?
Scenarios single- and multiplayer compatibile are almost always made with MP in mind and should be played as any other multiplayer mission. Copy mission's PBO to your MPMissions folder and start it from Multiplayer->Host menu.
Q: What do I do with a HTML preset?
Upon clicking a link for preset on A3M website you will be redirected to Arma Preset Creator which will list all the dependencies (except CDLCs!) of desired mission. Scroll down to the Download preset - (sizeGB) button, press it and wait until your HTML file downloads.
Next, open your Arma 3 Launcher and:
a) drag the file over Launcher and drop it
b) press More -> Import list from a file -> Select your preset, or
c) Click on PRESET in upper right corner of your Launcher, open the dropdown, click on Import button and choose your HTML file.
Best option is C) as it will save this preset in your dropdown and you will be able to switch between this and others you may have in the future.
Q: Can I edit the missions I downloaded?
Yes. You need PBO Manager or any similar software to unpack the downloaded PBO archive. Create a folder with the same name as said PBO (just do not add the .pbo part) and copy all files from PBO to that folder. Next, move your folder to your editing directory which can be C:\Users\username\Documents\Arma 3 - Other Profiles\YourName\missions for Singleplayer or C:\Users\username\Documents\Arma 3 - Other Profiles\YourName\MPMissions for Multiplayer. Campaigns store multiple scenarios within one PBO file so make sure you keep original names for said missions. You have to edit each of them individually.
Make sure you have correct mods loaded for editing, dependencies for playing may not be the same as dependencies for editing. Make sure you read all notifications and use correct mods.
Remember that any scenario is still someone's Intellectual Property. Editing it and releasing under your own name is considered stealing and may cause legal actions taken against you!
Q: Why is the mission/campaign I downloaded not working?
If you're confident you have placed the PBO file in proper place and you are starting your game only with required mods and DLCs, check generated RPT log file for any errors (you need to have -noLogs parameter deleted or unchecked in the Launcher). It will be located in AppData\Local\Arma 3\ directory, open the most recent one and search for warnings. If it's about missing dependencies, verify your mod list. If it's something else, better contact with content author. If nothing helps, you can join the Arma Archive Initiative Discord server.