How to use CFrame:Lerp() to move object?

So i've been wanting to use bezier curves, and i know you need to use :lerp() to move something along the curve. The problems is, I have no clue how to move using :Lerp(). Would you just move the position along the line made using :Lerp(), or is there another way of doing this?

I did do a script that creates a Bézier curve. I made this script a few years ago.I just went through it and updated it and it Should work. Your free to use/study the code.

Code:

local modelGrp = workspace:FindFirstChild("Stem Group")
if(modelGrp == nil) then
	modelGrp = Instance.new("Model",workspace)
	modelGrp.Name = "Stem Group"
end

function doStrand(name,firePos,TargPos,Properties,parent) 
	local Sides = {"Front","Back","Top","Bottom","Left","Right"}	
	local P = parent:FindFirstChild(name)
	if(P == nil) then 
		P = Instance.new("Part",parent)
		P.formFactor = "Custom"
		P.Transparency = 0 
		P.Reflectance = 0
		P.Name = name
		P.Locked = true
		P.CanCollide = false 
		P.Shape = "Cylinder"
		P.Anchored = true
		for i=1,#Sides do
			P[Sides[i].."Surface"] = "SmoothNoOutlines"
		end
		for k,v in pairs(Properties) do
			if(k ~= "Size") then
				P[k] = v
			end
		end
	end

	P.Size = Vector3.new((firePos - TargPos).magnitude,Properties.Size.x,Properties.Size.y) 
	P.CFrame = CFrame.new((firePos + TargPos)/2,firePos)*CFrame.Angles(0,math.rad(90),0)
	return P
end

function CalculateBezierPoint(t, p0, p1, p2, p3)
	local u = (1 - t);
  	local uu = u*u;
  	local uuu = uu * u;
	
	local tt = t*t;
  	local ttt = tt * t;
 
	local  p = uuu * p0; -- first term
	p = p + 5 * uu * t * p1; --second term
	p = p + 5 * u * tt * p2; --third term
	p = p + ttt * p3 --fourth term
 
  return p;
end



function ChangeV3(Pos,GtoPos,mod)
	local x = Pos.x	
	local y = Pos.y
	local z = Pos.z
	
	if(x > GtoPos.x) then if(x-mod < GtoPos.x) then	x = GtoPos.x else x = x -mod end
	elseif(x < GtoPos.x) then if(x+mod > GtoPos.x) then x = GtoPos.x else x = x +mod end 
	else x = x end

	if(y > GtoPos.y) then if(y-mod < GtoPos.y) then	y = GtoPos.y else y = y -mod end
	elseif(y < GtoPos.y) then if(y+mod > GtoPos.y) then y = GtoPos.y else y = y +mod end 
	else y = y end
			
	if(z > GtoPos.z) then if(z-mod < GtoPos.z) then	z = GtoPos.z else z = z -mod end
	elseif(z < GtoPos.z) then if(z+mod > GtoPos.z) then z = GtoPos.z else z = z +mod end 
	else z = z end
	return Vector3.new(x,y,z)
end

local Points = {
	Stem = {
		Pos = {Vector3.new(0,0,0),	Vector3.new(0,5,0),		Vector3.new(0,10,0),	Vector3.new(0,15,0)},
		Goals = {Vector3.new(0,0,0),Vector3.new(0,5,0),		Vector3.new(0,10,0),	Vector3.new(0,15,0)}	
	}
}

local createWeight = function(point,name)
	local CP = workspace:FindFirstChild(name)
	local Faces = {"TopSurface","BottomSurface","LeftSurface","RightSurface","FrontSurface","BackSurface"} 
	if(CP == nil) then 
		CP = Instance.new("Part",workspace)
		CP.Anchored = true
		CP.Name = name
		CP.FormFactor = "Custom"
		CP.Shape = "Ball"
		CP.Transparency = 0.4
		CP.Size = Vector3.new(2,2,2)
		for f=1,#Faces do
			CP[Faces[f]] = "SmoothNoOutlines"
		end
	end
	CP.CFrame = point
	return CP
end

local step = 0.1
local StemBaseSize = 2
local SEGMENT_COUNT = 50

local CPoints = {} 
for i=1,#Points.Stem.Goals do
	local name = (i >1 and i < 4) and "ControlPoint ["..(i-1).."]" or (i == 1) and "Start Point" or "End Point"
	CBrick = createWeight(CFrame.new(Points.Stem.Goals[i]),name)
	CPoints[i] = CBrick	
end
local myStyle = {
	BrickColor = BrickColor.new("Bright green"),
	Material = Enum.Material.SmoothPlastic,
	Size = Vector2.new(0.2,0.2),
	Shape = "Cylinder"
} 

local SIndex = 0

function scale(valueIn, baseMin, baseMax, limitMin, limitMax) 
   return ((limitMax - limitMin) * (valueIn - baseMin) / (baseMax - baseMin)) + limitMin;
end

function drawWeightLine(Goal,id)
	local myStyle = {
		BrickColor = BrickColor.Black(),
		Material = Enum.Material.SmoothPlastic,
		Size = Vector2.new(0.2,0.2),
		Transparency = 0.7
	} 
	local Segs = modelGrp:GetChildren()
	local Dist = math.huge
	local ClosestPoint = nil
	for i=1,#Segs do
		local dist = (Goal - Segs[i].Position).magnitude
		if(dist < Dist) then
			ClosestPoint = Segs[i]
			Dist = dist
		end
	end	
	if(ClosestPoint ~= nil) then
		doStrand("Weight Line ["..id.."]",ClosestPoint.Position,Goal,myStyle,workspace)
	end 

end

while true do
	local StemPos = Points.Stem.Pos
	local StemGoals = Points.Stem.Goals
	
	for i=1,#StemPos do

		StemGoals[i] = CPoints[i].Position
		step = (StemPos[i] - StemGoals[i]).magnitude/4
		StemPos[i] = ChangeV3(StemPos[i],StemGoals[i],step)

	end
	--print(StemGoals[2])
	for s = 0, SEGMENT_COUNT do
		local name = "Part "..s
	  	local t = s / SEGMENT_COUNT;
	  	local tu = (s >0) and (s-1) / SEGMENT_COUNT or 0

		pixel = CalculateBezierPoint(t, StemPos[1], StemPos[2], StemPos[3], StemPos[4]);
		Prev = CalculateBezierPoint(tu, StemPos[1], StemPos[2], StemPos[3], StemPos[4]);
		Seg = doStrand(name,pixel,Prev,myStyle,modelGrp)
	end
	for i=1,#StemGoals do
		drawWeightLine(StemGoals[i],i)
	end

	SIndex = (SIndex < SEGMENT_COUNT) and SIndex+1 or 0

	wait()
end

The script runs creates a vertical line with 4 spheres acting as weights. Move the spheres and you'll see the Line move, kinda like the Photoshop Bézier curve tool.

If I had a chance to re-make the script it would be a lot neater as I was learning to code at the time I made this script so sorry for the mess lol.

I was thinking you could rather than create the vertical line you could record the positions as if they were a path.

Hope this helps!

Thanks for the help! That link helped me figure it out. I basically just change the position between two points using CFrame:Lerp() in a for loop. To do the curve, i just plugged the time and others parameters into the function through an equation and move the object there. I honestly dont understand how the equation works, but at least I know how to use curves now. Thanks for the help!