Scripts talking between eachother?

Roblox has four different objects that allow for cross script communication, there is some great documentation on some of these, but I will try to do my best to break them down for you.

Bindable Events

A BindableEvent is an object that has two important cross communication properties. The first of the two is :Fire(...). This function will trigger the BindableEvent. This is then detected by the next important property, .Event.

It is important to note that these can only communicate between scripts of the same scope (server to server or client to client)

First Script

BindableEvent:Fire(argument)

Second Script

BindableEvent.Event:connect(function(argument)
    --code
end)

Bindable Function

A BindableFunction is very similar to a BindableEvent, however it allows you to return a value back to the script that Invoked the function. One script will use the function :Invoke(...) in order to trigger the BindableFunction. The other script will detect this with it's event .OnInvoke, however something must be returned.

It is important to note that these can only communicate between scripts of the same scope (server to server or client to client)

First Script

local something = BindableFunction:Invoke(argument)

Second Script

BindableFunction.OnInvoke:connect(function(argument)
    --code
    return something
end)

Remote Event

A RemoteEvent is very similar to a BindableEvent except it allows for cross scope communication (server to client or client to server). If you want to trigger an event on the server from a client script, you would use the function :FireServer(...). If you want to trigger an event on the client from a server script you would use :FireAllClients(...) or if you want it to only fire for a specific client you would use:FireClient(player, ...). The event is received on the server with .OnServerEvent (note that an argument of player is automatically sent) or on the client with .OnClientEvent .

Server Script

RemoteEvent:FireClient(player, argument)

Client Script

RemoteEvent.OnClientEvent:connect(function(argument)
    --code
end)

Remote Function

A RemoteFunction is very similar to a RemoteEvent but, like a BindableFunction, allow a value to be returned to the triggering script. To trigger the server you use the function :InvokeServer(...) and to trigger the client you use :InvokeClient(player, ...) (note there is no InvokeAllClients function). The function is received on the server with .OnServerInvoke (note that an argument of player is automatically sent) and on the client with .OnClientInvoke. Remember that something must be returned.

Client Script

local something = RemoteFunction:InvokeServer(argument)

Server Script

RemoteFunction.OnServerInvoke:connect(function(player, argument)
    -- code
    return something
end)