1: Escape Kerbin SOI 2: Set asteroid as target 3: Shoot prograde (assuming the asteroid is coming from a more distant orbit) until you cannot get the approach any closer 4: Adjust your plane (using the pink maneuvre tools) to put a node on top of the closest approach. This can be done in combination with step 2. 5: It is going to be very difficult to get closer than like 20,000km at first because every slight engine burst will change the distance tremendously. Once you are relatively close though, warp forward to a closer point and adjust your trajectory again using the maneuvre tool to try and get closer to the roid. The closer to the roid, the less sensitive the periapsis is to engine bursts. 6: Repeat step 5 until you have a periapsis maybe 10km from the asteroid. 7: Warp until the distance to the asteroid is around 100km. Click on the velocity on top of the nav ball until it displays your velocity relative to the target velocity. This will be around 1500 m/s. Point the ship retrograde (while still having the navigation relative to the target) and brake. Depending on the power of your engines, you may want to break earlier or later than 100km. We want to have elimated our relative velocity to the target as close to the periapsis as possible. Brake repeatedly to maintain control and reduce the velocity, so that when the distance to the asteroid starts to increase rather than drop, you can nullify the relative velocity completely. 8: Once the relative velocity is 0 m/s, point towards the target and fire to maybe 50m/s - then turn the ship retrograde ready to brake again. 9: Once once the distance to the roid again starts to increase rather than drop (or if you randomly actually exactly hit it and are getting to close to it), kill the relative velocity again. 10: Repeat step 8 and 9 again (but with less speed and more care the closer you get) until you are close enough to the roid to use rcs. 11: Click the roid, right click and select Target centre of mass. 12: If you are in doubt where to push it, approach it and grab it from the sun side, so you won't run out of power. 13: Deploy the grabbing tool and target the centre of mass - hit the roid with around 0.5m/s or less. 14: If your prograde node now doesn't allign with the target node, the asteroid will spin if you start your engines. You can right click the grabbing tool and select "release pivot" and adjust your prograde so they allign. Then relock it. 15: Happy pushing.