The short answer: get to Kalanki junction on the Ring Road, then take any westbound bus or microbus marked for Thankot, Chandragiri or Naubise. The second leg costs roughly NPR 20 to 35 and takes 20 to 40 minutes outside peak hours. Tell the conductor you want the Chandragiri cable car and he will set you down on the Tribhuvan Highway at the access road, about 15 to 25 minutes walk below the base station.
If you would rather not do it in two stages, a taxi from central Kathmandu runs about NPR 800 to 1,500 one way, and a ride-hailing car through Pathao, InDrive or Yango usually prices between NPR 600 and 1,200. All three take 30 to 45 minutes when the road is moving and 60 to 90 minutes when it is not.
Thankot sits 12 km west of central Kathmandu at the western rim of the valley, in Chandragiri Municipality. It is the point where the Tribhuvan Highway enters the Kathmandu Valley, which is both why it matters historically and why the approach road carries every freight vehicle arriving from the west. Plan around the traffic, not the distance.