First of all, to make a harpoon, use a grabber that can attach to immobile objects, so you can use it to climb things in the sandbox
There are a few efficient methods on how to make a harpoon system, but it all depends on where and how you want to put it.
A good way of propelling a harpoon using standard besiege requirements (meaning no mods) is making a spring-loaded slingshot. You probably know how to make one, just make a pipe with the harpoon inside, which is binded to the front of the pipe with springs. just press your designated fire button and watch your harpoon shoot off. Just don't forget to have the harpoon linked to your vehicle with a rope and winch.
2. (my favorite method) Railgun
This does require Nobounds (sorry) unless you find a glitch to propel the harpoon at light speed legitimately. What this uses is the same harpoon in a pipe, except it's attached to the back of the pipe by a few slider blocks. Then you have two flying spirals on the outer sides of the pipe connected via braces to the back of the harpoon on the inside. Adjust their flying speed to about 40x and fire. Your harpoon should normally slide out of the pipe in no time (literally) and probably be more of a WMD than a harpoon.