Rotating around a point?

CFrame

A simple implementation of CFrame.Angles will do the trick. CFrame.Angles returns a rotation with 3 given axes (X,Y,Z), in radians.

Radians overview

In case you don't know how radians work, I'll provide a quick overview. Radians are basically a different form of measurements for a circle (oppose to degrees). But, they can work the same way. An example of radians you're probably familiar with is Pi (3.14...) which represents half a rotation in radians. Therefore 2*Pi = 360 degrees, which is a full circle in radians (6.28...)

Anyway, with that out of the way, I'll give you an example:

local Point = CFrame.new(0,10,0) -- The point the object will rotate around
local Offset = CFrame.new(0,0,10) -- the offset of the part (distance from it)

local Object = Instance.new("Part",workspace)
Object.Anchored = true

while true do

	-- Each iteration, we're making the Object's CFrame equal to the Point's CFrame, multiplied by the rotational CFrame, then again multiplied by the offset.

	-- "math.rad" simply converts it's numeric argument to radians.

	for i = 1,360 do
		Object.CFrame = Point * CFrame.Angles(0,math.rad(i),0) * Offset
		wait()
	end
end

Note

I'm not gonna cover the entire CFrame library, so if you're not experienced in it, I suggest this wiki page: http://wiki.roblox.com/index.php?title=CFrame#Constructors

Hope this helped, let me know if you have any questions.