How does AI Pathfinding work?

Well path finding is basically a way to get to point A to point B, also there is no "better method" out of all the methods, because they do the same thing.

So I went on studio's and took a zombie AI script and thought I could break it down trying to show you how an AI works, I guess you can make your own path find method but there all similar in someway.

local larm = script.Parent:FindFirstChild("Left Arm")
local rarm = script.Parent:FindFirstChild("Right Arm")

function findNearestTorso(pos)
    local list = game.Workspace:children()
    local torso = nil
    local dist = 1000
    local temp = nil
    local human = nil
    local temp2 = nil
    for x = 1, #list do
        temp2 = list[x]
        if (temp2.className == "Model") and (temp2 ~= script.Parent) then
            temp = temp2:findFirstChild("Right Arm")
            human = temp2:findFirstChild("Humanoid")
            if (temp ~= nil) and (human ~= nil) and (human.Health > 0) then
                if (temp.Position - pos).magnitude < dist then
                    torso = temp
                    dist = (temp.Position - pos).magnitude
                end
            end
        end
    end
    return torso
end




while true do
    wait(math.random(1,5))
    local target = findNearestTorso(script.Parent.Torso.Position)
    if target ~= nil then
        script.Parent.Humanoid:MoveTo(target.Position, target)
    end

end

So that's the script now let's break it down.

Part

local list = game.Workspace:children()
    local torso = nil -- This is defining if the torso that it's trying to find is equal to nil.
    local dist = 1000 -- MaxDistance that it can find the Torso.
    local temp = nil -- Will later be explained and so is the bottom.
    local human = nil
    local temp2 = nil

Part2

for x = 1, #list do -- For the number of children of workspace and was defined in Part1
        temp2 = list[x]  -- Saying that Temp2 is equal to every child of workspace
        if (temp2.className == "Model") and (temp2 ~= script.Parent) then -- Now it's only narrowing it down to models and if the child is not script's parent(zombie)

Part3(Final)

temp = temp2:findFirstChild("Right Arm") -- Finding right Arm of the player in workspace
            human = temp2:findFirstChild("Humanoid") -- Remember Temp2 is every model and a player's cahracter is a model the rest is self explanatory
            if (temp ~= nil) and (human ~= nil) and (human.Health > 0) then -- If the player right are is not equal and the humanoid is not equal to nil and the humanoid's health is greater then 0
                if (temp.Position - pos).magnitude < dist then -- If the position of the players - zombie's magnitude is less then the dist
                    torso = temp -- the torso now equals temp
                    dist = (temp.Position - pos).magnitude -- the dist variable is now equal to zombie - player's magnitude.
                end
            end
        end
    end
    return torso -- returns it
end

Hope this help's.

There's really no one answer to this question. It depends on how your maps are made, how your game plays (i.e. weapon design) and countless other things.

Your 'markers' are typically called Nodes, by the way.

Here are the four pathfinding pages on the wiki. I suggest you just go for it and ask for help here when you get stuck. :>