I do not understand how to make a script that fires a remote event from server - client?

Yeah, it's optional this remote event gets fired instantly when the player joins the game.

Firing to client

You can also do this remoteEvent:FireClient(game.Players.MarkedTomato) .

or

Use a TouchedEvent which does

local part = workspace.Part

part.Touched:Connect(function(objectThatTouchedMe)
    if objectThatTouchedMe.Parent:FindFirstChild("Humanoid") then
        local client = game.Players:GetPlayerFromCharacter(objectThatTouchedMe.Parent)
        remoteEvent:FireClient(client)
    end
end)

--[[
line 5 game.Players:GetPlayerFromCharacter which just gets the player from the character I also added a sanity check to see if objectThatTouchedMe.Parent has a humanoid which is the character model.
line 6 just fires the remote event to the client
]]

There are probably more methods of firing to the client.

Firing to Server

LocalScript

local remoteEvent = game:GetService("ReplicatedStorage").RemoteEvent

local str = "Server"

remoteEvent:FireServer(str)

ServerScript

local remoteEvent = game:GetService("ReplicatedStorage").RemoteEvent

remoteEvent.OnServerEvent:Connect(function(playerThatItGotFiredFrom, str)

    print(str)
end)

So in the LocalScript, I just pass the string value into the parentheses. On the server, the first parameter is the player even though I didn't define it Roblox automatically gives me the player that it got fired from so you DON'T need to define the player. I've seen so many people define the player in the LocalScript which you don't need to do. So our first parameter in the LocalScript will be the second in the ServerScript.

Firing to all clients

You can only do this from the Server. This function works exactly like :FireClient() but you don't need to define the player since you're firing to all clients. It works like the Server since all clients experience the same thing all at once.

ServerScript

local remoteEvent = game:GetService("ReplicatedStorage").RemoteEvent

local str = "test"
remoteEvent:FireAllClients(str)

LocalScript

local remoteEvent = game:GetService("ReplicatedStorage").RemoteEvent


remoteEvent.OnClientEvent:Connect(function(str)
    print(str)
end)

This will print 'test' in all client's outputs.

Any questions? Just reply to my answer.