How do I make a capture script for a King Of The Hill (teams) game?

I suggest you use Region3 to check who currently on the hill.

local charTable = {}
local inHillRegion = {}
local zone = workspace:FindFirstChild("Capture").Capture
local pos1 = zone.Position - (zone.Size/2)
local pos2 = zone.Position + (zone.Size/2)
local region = Region3.new(pos1,pos2)

while wait() do
	inHillRegion = nil
	local partsInRegion = workspace:FindPartsInRegion3(region,charTable,1000)
	for i,v in pairs(partsInRegion)do
		local thisChar = v.Parent
		local player = game.Players:GetPlayerFromCharacter(thisChar)
		if inHillRegion[player.UserId] = nil then
			inHillRegion[player.UserId] = thisChar
		end
	end
	--Do anything you want to the players in here
end

game.Players.PlayerAdded:Connect(function(player)
	player.CharacterAdded:Connect(function(char)
		charTable[player.UserId] = char
	end)
	player.CharacterRemoving:Connect(function()
		charTable[player.UserId] = nil
	end)
end)

I havent tested this but it might work

Edit* if you still need it, heres the working script. Make sure you put it in the capture zone part

local inHillRegion = {}
local zone = script.Parent
local pos1 = zone.Position - (zone.Size/2)
local pos2 = zone.Position + (zone.Size/2)
local region = Region3.new(pos1,pos2)

while wait(.5) do
    inHillRegion = {}
    local partsInRegion = workspace:FindPartsInRegion3(region,nil,500)

	for i,v in pairs(partsInRegion)do
		if v.Parent:FindFirstChild("HumanoidRootPart") and v.Parent:FindFirstChild("Humanoid") and v.Parent:FindFirstChild("Head") then
			local player = game.Players:GetPlayerFromCharacter(v.Parent)
			if inHillRegion[player.UserId] == nil then
				inHillRegion[player.UserId] = v.Parent
			end
		end
	end
	for i,v in pairs(inHillRegion)do
	    --Do anything you want to the players in here
	end
end