How can I change the walk speed of the player?

I don't know how you want to increase the player's speed, for example it happens when you touch a brick or a key bind. Since you're using a server script, you're trying to access the LocalPlayer, but that's only available through local scripts, not server. Either you can put your original code in a local script, or you can do this:

game.Players.PlayerAdded:Connect(function(plr)--This happens whenever a player joins

    local char = plr.Character or plr.CharacterAdded:Wait()--Gets player's character
    local hum = char.Humanoid
    hum.WalkSpeed = game.ReplicatedStorage.Points.Value + 3

end)

This code goes in a normal script. Put this script in ServerScriptService. I also noticed you're trying to set the WalkSpeed from the character. It's the character's humanoid that you do this to, not the actual character.

local localPlayer = game.Players.LocalPlayer
localPlayer.Character.Humanoid.WalkSpeed = game.ReplicatedStorage.Points.Value + 3

You were using the local as "LocalPlayer"

so it diden't know what to use. , also you need to use a Humanoid