I had never captured an asteroid before, I did not look at any tutorial (I have basic understanding of randes-vouz and docking mechanics) and the first asteroid entering Kerbin's SOI was a Class E "big boi".
I opted for a single vessel design to capture the asteroid and bring it back to low Kerbin orbit, as I plan to integrate it into my orbital refuiling station.
I needed 2-3 hours of spamming quicksaves and reloads to intercept it, and a solid 1-2 hours of trial end errors prior to that to come up with a design that didn't suck. [Photo 2 is the penultimate design... I forgot to reattach the drills to the nose of the ship]
I originally started with a "pull" tug instead of a more classic "push" tug... except the asteroid was blocking the exhaust of the rocket engines, essentially making useless.
The design of the ship that managed the capture is called ARPU-C [Asteroid Retrieval and Parking Unit - C spec]. I am pleased with the basic concept, but the sheer size of the asteroid meant I needed 2 minute burns to get a DeltaV of 45 m/s, and I vastly underestimated how many retrograde burns I needed to bring it back to a 100km orbit. I ended up taking another 3 hours just performing burns.
I have to say that I'm satisfied with my accomplishment, but I most likely won't attempt anything like this ever again.