How do I bind "W" to jump using scripts?

It's not very complicated. You just need to understand how to get a player's keypress and need to understand remote events.

Make sure this is a local script inside of startergui:

--LOCAL SCRIPT
--PUT THIS SCRIPT INSIDE OF STARTERGUI

local player = game.Players.LocalPlayer
local character = player.Character or player.CharacterAdded:Wait()
local humanoid = character:WaitForChild("Humanoid")
local mouse = player:GetMouse()

local jumpEvent = game:GetService("ReplicatedStorage"):WaitForChild("jumpEvent") --Waits for the remoteEvent to be created by the server

mouse.KeyDown:Connect(function(key)
	if string.lower(key) == "w" then
		jumpEvent:FireServer() --send a message to the server to tell the player to jump
	end
end)

Make sure this is a server script:

--SERVER SCRIPT

local jumpEvent = Instance.new("RemoteEvent", game:GetService("ReplicatedStorage")) -- create the remoteEvent
jumpEvent.Name = "jumpEvent"

jumpEvent.OnServerEvent:Connect(function(player) -- receive the message from the local script
	print("Jumped")
	player.Character.Humanoid.Jump = true
end)

The reason we need two scripts is because server scripts cannot get a player keypress and local scripts cannot make the player jump. So we use the remote events to let them communicate to each other.