I know what you mean ... it took us a while (and getting lost a few times) to figure it out. There's a walkway on the second level of the Station that connects the two sides. As you enter the Station from the north side (opposite Kyoto Tower), the central gates are straight ahead. To your right, there's an escalator (and stairs) that take you up to the second level (and if you keep going up the escalators, all the way up to the 11th floor). When you get up to the second level, zig-zag to the left (past a couple of cafes on the left) and at the end of the short passageway, turn left into the central walkway. That will take you all the way over to the Hachijo side - when you get to the far end of the walkway, there's a short escalator back down. The Shinkansen gates will be on your left, the Kintetsu line gates on your right and the Hachijo exit straight ahead.

This page of Kyoto Station information provides some photos. The third photo shows the walkway. In the first photo, you can see that initial escalator towards the bottom right of the photo, with the zig zag to the left on the second level (so you don't continue on up the escalators). On the Karasuma (north) side of the Station, the walkway ends with stairs (and an escalator on each side) down to the Station forecourt (to the east of the central entrance opposite Kyoto tower).

I understand your pain. We made the mistake (several times...) of going down to try and get from one side to the other, only to get totally lost in the labyrinth underneath the Station.