Making a admin gui but i can't seem to get it the text in the command box right?

There are quite a lot of problems here that need to be looked at:-

1. Both scripts should not be trying to get the player object as any changes need to be done on the server side (All checks should be done on the server even if you check them on the client side as well). The player object is passed as a parameter when the event is received on the server.

2. Based upon the fact that you have local event = screen:WaitForChild("Event") this suggests that the event is inside the gui, this is not a good place to put the event as you would need to connect the event each time the gui is added from the server side as it is delete when the player dies. It is best to put this remote event into the ReplicatedStorage.

3. Cmds.Visible = true and list.Visible == false and history.Visible == false the and operator is used to compare variable. You need to set the value not compare them e.g. == is a comparison and = is an assignment.

4. As nicemike40 has mentioned you are not firing the event, you are trying to fire the text parameter??

Other points:-

It is not a good idea to use the players name as users can change them, use UserId as this cannot be changed and will allow users to change their name while still being an admin.

The fix (local script):-

---Player things
local mouse =  game.Players.LocalPlayer:GetMouse()

---Services
local uis = game:GetService("UserInputService")

--- Guis, you may want to add in WaitForChild as there may be a small delay when replicateing the gui to the client
local screen = script.Parent
local Cmd = screen.CmdBox
local execute = screen.Run
local maingui = screen.Gui
local mainframe = maingui.Frame
local history = mainframe.ChatHistory
local list = mainframe.AdminList
local Cmds = mainframe.Commands
local history1 = mainframe.ChatHistory1
local list1 = mainframe.AdminList1
local Cmds1 = mainframe.Commands1
local expla = mainframe.Explanation

--Event
local event = game:GetService('ReplicatedStorage'):WaitForChild('') -- add event name

uis.InputBegan:connect(function(input)
    if input.KeyCode == Enum.KeyCode.BackSlash then
        Cmd:CaptureFocus()
    end
end)

history1.MouseButton1Down:connect(function()
    history.Visible = true  -- we use assignments
	list.Visible = false 
	Cmds.Visible = false
end)

list1.MouseButton1Down:connect(function()
    list.Visible = true 
	history.Visible = false 
	Cmds.Visible = false
end)

Cmds1.MouseButton1Down:connect(function()
 	Cmds.Visible = true
	list.Visible = false 
 	history.Visible = false
end)

execute.MouseButton1Down:connect(function()
    if Cmd.Text ~= '' then -- we need to check for a blank/empty string
		event:FireServer(Cmd.Text)
    end
end)

Server Script ( in ServerScriptService):-

--Event
local event = game:GetService('ReplicatedStorage'):WaitForChild('') -- event name here

--- Admins
local admins = {["Player1"] = true, ["Player"] = true, ["yougottols1"] = true, ["Cyber_Monkey"] = true}

event.OnServerEvent:connect(function(plyr, Trying)
    print('Fired by', plr, 'data sent', Trying)
end)

Example not using player name:-

--Event
local event = game:GetService('ReplicatedStorage'):WaitForChild('') -- event name here

--- Admins
local admins = {[player id here]= true, [player id here] = true, [player id here] = true}

event.OnServerEvent:connect(function(plyr, Trying)
	if admins[plyr.UserId] then -- user is in the list
   	 	print('Fired by', plr, 'data sent', Trying)
	else
		print('not admin')
	end
end)

I hope this helps, please comment if you do not understand how / why this code works.