How do I deal with a leaking toilet cistern inlet pipe?
Are you sure it's actually leaking from the bottom seal and not just flowing down from the top seal connected to the cistern? To be sure run your dry hand around the pipe near the top seal.

In any case to replace any of those seals:


Turn off the inlet tap to the cistern and flush until no more water remains in the cistern.  (Have some rags ready anyway as there's bound to be a small amount of water coming out residual to the cistern.) 
Undo the nut at the cistern end by hand and lower this end of the pipe--now you can slide it back towards the cistern to remove it from the bowl. 
Replace any broken seals and reinstall (reverse of removal instructions). 
Open the water to cistern inlet and flush several times to check for leaks. Make sure both the cistern and bowl are well secured as any possible movement left may cause leak during usage.