how do you actually counter karthus?

Mobility is Karthus’ biggest weakness, especially in the early game. If you are constantly moving during your attack patterns and making sure to change your approach so you don’t become predictable you can negate a lot of his impact inlane.

As far as his R is concerned there is a very special item called Banshees Veil. If you are a caster champion I highly recommend getting that early on. You could also purchase a Zhonyas if you aren’t sure that you’ll survive the damage.

Aside from those two options the only thing I can suggest is building Magic Resist, forcing Karthus to invest heavily in magic penetration. It may not seem like it helps but I assure you it does.

MR items Abuse his early , he doesn't do much damage in early unless he hits a lot of Q's , they aren't hard to dodge