Storyline Missions (LW2)
The Long War 2 campaign is a little different to vanilla, particularly in the early stages.
There is no tutorial and you always begin dropping in to a mission to ambush a troop column. After that you'll go to the Geoscape, with 2 main objectives - liberate a region and research Alien Biotech.
Liberating a Region
Unlike vanilla, where the Blacksite is presented to you after a short time, in Long War 2 your first objective is to liberate a region. You start this by setting haven rebels to the Intel job and detecting a liberation 1 mission, which will be a hack or recover mission with a Find a Lead reward, but no Intel Package listed. This will silently cause Liberation 2 missions to spawn in that region, which you must again detect with rebels on the Intel job.
Liberation 2 and 3
After completing liberation 1 you need to keep scanning for liberation 2, which will be clearly marked as a liberation mission, and will be a VIP extraction or rescue. This will be a little harder than usual. After that, liberation 3 will spawn, which is also clearly marked as a liberation mission and will be a VIP assassination or destroying a relay, and will also be harder than usual. Finding and completing liberation 1 to 3 may take some time, so it's likely that you'll make some progress contacting other regions and building up your force before you manage it. You can liberate any region, it doesn't need to be your starting one.
Regional Network Tower
After liberation 3, you'll unlock the network tower assault for that region. Regional network tower assaults are quite difficult missions, with a soft timer where reinforcements will appear more and more rapidly until you hack the objective. You then need to eliminate all enemies. Completing your first network tower assault reveals information about the Avatar Project, including the doom clock, and allows finding and assaulting alien research facilities. It also reveals the ADVENT regional HQ and allows you to assault it.
Regional HQs have a lot of powerful enemies, but no time limit, so bring your big guns and take it slow and eliminate all enemies. Completing your first liberation reveals an alien Blacksite in an uncontacted region.
The Long War Blacksite mission is very similar to the vanilla version. You must contact the region it's in to attempt it, then infiltrate the mission to 100% before you can launch it. You then either fight or stealth your way in to the facility (though accomplishing this mission entirely through stealth is likely to be very difficult), steal a vial of an alien substance, then extract. There are no reinforcements in this mission until you approach the vial, so you can take it slow right up to the end. After grabbing the vial, head to the extraction zone at the back and exit.
The Blacksite vial needs to be researched in the Shadow Chamber. Once researched it unlocks the Forge mission.
Completing the Blacksite knocks back the Avatar Project by 3 blocks.
The Forge mission will spawn after you research the Blacksite vial. You need to contact the region it's in before it can be assaulted, and you must infiltrate to 100% before you can launch.
You must enter the alien facility and steal the Forge Suit, then call for extraction and extract the suit. This mission can technically be done as a stealth mission, but given the number of enemies that will be very difficult to do. There is no timer or reinforcements until after you steal the suit, so the alternative of going in heavy and taking it slow will probably be easier.
Stealing the Forge Suit knocks back the Avatar Project by 3 blocks, and allows researching the Forge Suit in the Shadow Chamber, which is a prerequisite for the Avatar Autopsy.
Alien Biotech and Skulljacking
Also available at the beginning of the game is the Skulljacking plot line. First you must research Alien Biotech, then autopsy an ADVENT officer. This reveals information about the implants ADVENT uses to control its troops. After this you'll be directed to build a Proving Ground and build the Skulljack, then use it on an officer in the field. This will spawn a Codex. Killing the Codex will drop a Codex Brain (which you will collect even if extracting), which can be researched in the Shadow Chamber.
Researching the Codex Brain will direct you to skulljack a Codex in the field. It will also reveal the coordinates of an alien Psi-Gate.
Killing the Codex knocks back the Avatar Project by 3 blocks.
Assaulting the Psi-Gate
The Psi-Gate mission will spawn after you research the Codex Brain in the Shadow Chamber. You need to contact the region it's in and then infiltrate the mission to 100% before you can launch. This mission has no time limit or reinforcements, but has a lot of enemies, and you must eliminate them all.
The Shadow Chamber must be upgraded to research the Psi-Gate. Researching the Psi-Gate is a prerequisite for autopsying the Avatar corpse.
Capturing the Psi-Gate knocks back the Avatar Project by 3 blocks.
Skulljacking a Codex
After researching the Codex Brain you'll be directed to skulljack a Codex in the field. Doing this will cause an Avatar to teleport in. Killing the Avatar allows you to recover an Avatar corpse (which you'll recover even if you extract from the mission).
Killing the Avatar knocks back the Avatar Project by 3 blocks.
Autopsy the Avatar
You can only autopsy the Avatar corpse after you've completed research on the Forge Suit and Psi-Gate. Researching the Avatar corpse then opens up the end-game sequence.
Central Network Tower
The Avatar Project starts off hidden, so you've little idea of how far the aliens are progressing. The doom clock will be revealed after completing your first regional network tower assault as part of the liberation quest line. For reference, with no knock backs of the doom counter, you can expect to lose the campaign after approximately 8 months.
Knocking back the doom clock can be done by completing story objectives, each of which usually knocks back the doom clock by 3 pips. It can also be knocked back by destroying ADVENT research facilities that are housing doom pips.
After revealing the doom clock, you'll be able to detect and attack alien research facilities. When a facility produces a doom pip, you'll be informed where that facility is, which can help planning which regions to contact. To attack a facility you need to contact the region it's in and get a Facility Lead (these can be obtained from missions that Find a Lead, or from skullmining ADVENT troops), then research it. To assault a facility you must infiltrate the mission to 100% or more to launch. You begin in stealth and must get to the object, plant the X4 charges, and at least one soldier must successfully extract, then the facility will be destroyed.
Destroying a facility will remove any doom pips that facility had. Note that facilities will occasionally transfer their doom pips to the global doom counter, at which point you can't remove them except by completing story objectives.
The Avatar Project can also be passively hindered by greatly succeeding at missions over the campaign. If the global vigilance level is greater than the global alert level then Avatar Project progress will be slowed as the aliens pay more attention to security, the effect of which can be seen in the Resistance Management screen. In addition, the aliens will always build 3 research facilities, but will be reluctant to build more if XCOM is succeeding at missions. If XCOM isn't doing enough to keep the aliens busy, they will build more research facilities for Avatar.