A basic walkthrough of a grid placement system?

I know this is a year old but I thought I could help anyway.

First you want to create a function to do the movement. To move a part to the mouse position you use Mouse.Hit. I am creating three variables one for each axis. Also I am creating two functions that will be used later on in the script. Make a simple model with a primary part so that we can move the model around in our space.

-- Define variables
local Player = game.Players.LocalPlayer
local Mouse = Player:GetMouse() -- Gets the mouse

local PosX -- X
local PosY -- Y
local PosZ -- Z

local Model = game.ReplicatedStorage.Model:Clone() -- Model you have ready

-- Main script

local function Snap()
    --Sets variables

    PosX = Mouse.Hit.X
    PosY = Mouse.Hit.Y
    PosZ = Mouse.Hit.Z
end

local function Movement()
    Mouse.TargetFilter = Model --Ignores the model

    Snap()  -- Gets the variables ready (We will snap later)

    Model:SetPrimaryPartCFrame(CFrame.new(PosX, PosY, PosZ)) -- Moves the model
end

-- Starts placement
local function StartPlacement()
    Model.Parent = workspace
end

game.Players.PlayerAdded:Connect(StartPlacement) -- Simple so not explaining this

To snap to a grid we round either up or down to the nearest whole. math.floor()and math.ceil() will work for snapping. math.floor() rounds down and math.ceil() rounds up

-- Define variables
local Player = game.Players.LocalPlayer
local Mouse = Player:GetMouse() -- Gets the mouse

local PosX -- X
local PosY -- Y
local PosZ -- Z

local Model = game.ReplicatedStorage.Model:Clone() -- Model you have ready

-- Main script

local function Snap()
    --Sets variables

    PosX = math.floor(Mouse.Hit.X) -- SNAP
    PosY = Mouse.Hit.Y
    PosZ = math.floor(Mouse.Hit.Z) -- SNAP
end

local function Movement()
    Mouse.TargetFilter = Model --Ignores the model

    Snap()  -- Gets the variables ready (We will snap later)

    Model:SetPrimaryPartCFrame(CFrame.new(PosX, PosY, PosZ)) -- Moves the model
end

-- Starts placement
local function StartPlacement()
    Model.Parent = workspace
end

game.Players.PlayerAdded:Connect(StartPlacement) -- Simple so not explaining this

You will notice that the model is snapping but only on a 1x1x1 grid. To add grid size it gets a little more complex (not really though). First you divide the mouse pos by the grid then add 0.5 then round and finally multiply by grid size. Example:

-- Define variables
local Player = game.Players.LocalPlayer
local Mouse = Player:GetMouse() -- Gets the mouse

local PosX -- X
local PosY -- Y
local PosZ -- Z

local GridSize = 2 -- Example

local Model = game.ReplicatedStorage.Model:Clone() -- Model you have ready

-- Main script

local function Snap()
    --Sets variables

    PosX = math.floor(Mouse.Hit.X / GridSize + 0.5) * GridSize -- SNAP
    PosY = Mouse.Hit.Y
    PosZ = math.floor(Mouse.Hit.Z / GridSize + 0.5) * GridSize -- SNAP
end

local function Movement()
    Mouse.TargetFilter = Model --Ignores the model

    Snap()  -- Gets the variables ready (We will snap later)

    Model:SetPrimaryPartCFrame(CFrame.new(PosX, PosY, PosZ)) -- Moves the model
end

-- Starts placement
local function StartPlacement()
    Model.Parent = workspace
end

game.Players.PlayerAdded:Connect(StartPlacement) -- Simple so not explaining this

This is the simplest way to snap to a grid. Hope this helps (if you see this.)