How do I get this script to find the total number of a certain team?

Here's a script that does what you asked and a little neater:

local team = game.Teams;

function getPlayers(teamColor) -- team color is easier than name
    local found = { };
    for _,v in pairs(game.Players:GetPlayers()) do
        if v.TeamColor == teamColor then
            table.insert(found, v)
        end
    end
    return #found
end

repeat -- SEE NOTE AT BOTTOM
    wait() until getPlayers(BrickColor.new('Bright red')) == 0
              or getPlayers(BrickColor.new('Bright yellow')) == 0
              or getPlayers(BrickColor.new('Bright green')) == 0
              or getPlayers(BrickColor.new('Bright blue')) == 0


-- do stuff

NOTE: Using a repeat will STOP once one is detected to be true. You can remove, add, or use and statements if you like.

Your problem is that you're never recalculating the team. So it the table will always return the same results as when you first defined it. To fix this, define the table in the loop.

Here's an example of a more efficient code;

local teams = game.Teams:GetChildren()

function getPlayers(team)
    local t = {}
    for i,v in pairs(game.Players:GetPlayers()) do
        if v.TeamColor == team.TeamColor then
            table.insert(t,v)
        end
    end
    return t
end

while wait() do
    for i = 1,#teams do
        local tab = getPlayers(teams[i])
        if # tab == 0 then
            print(teams[i].Name..' Team Died')
        end
    end
end