How would I use a remote event in this script to fire a cutscene, I really need help on this?

You can fire remote events to do communication in client - server, server - client and more! For example, lets make a player gui that makes a server side part.

To start, you can put your remote event in ReplicatedStorage.

Add a script to serverscriptservice, that defines what the remote will do when it gets fired.

local Remote = game.ReplicatedStorage.Remote

Remote.OnServerEvent:Connect(function(Player,Color) --You can insert multiple parameters here, keep in mind the first parameter is always the player
     local NewPart = Instance.new("Part")
     NewPart.Parent = workspace
     NewPart.Color = Color
end)

Now that we are done, make a localscript on a button, when pressed it will fire the remote:

script.Parent.MouseButton1Click:Connect(function() --Click event
      game.ReplicatedStorage.Remote:FireServer(Color3.fromRGB(255,255,0))
end)

As a result, the player will make a new part visible to all players on the server!

If you want to communicate server to client, you can insert a localscript in StarterPlayerScripts that will define what it will do:

(We will do if the player touches a brick, it will create a text label to it, Note: I already know there are other ways on how to do this,but this is just to test remote events)

game.ReplicatedStorage.Remote.OnClientEvent:Connect(function(Player,Color)
       local TL = Instance.new("TextLabel")
       TL.Parent = Player:WaitForChild("PlayerGui").ScreenGui
       TL.BackgroundColor3 = Color
end)

Now on the brick, instert a server script, to call the function

script.Parent.Touched:Connect(function(Hit)
     local Human = Hit.Parent:FindFirstChild("Humanoid")
     if Human then
           local Player = game.Players:GetPlayerFromCharacter(Hit.Parent)
           game.ReplicatedStorage.Remote:FireClient(Player,script.Parent.Color)
     end
end)

If you want to make it for all clients, re-write the remote event line and change it to:

game.ReplicatedStorage.Remote:FireAllClients(script.Parent.Color)

Hope it helps!