Attach a length of PVC pipe to the outlet of your air conditioner's P-trap with a pipe connector. Then, run multiple lengths of pipe from your air conditioner's condensate outlet to your sink, using connectors to join them.
Connect a length of rubber drainage hose to the end of your PVC piping when you've reached the area under your sink. Use a hose clamp to secure it into position.
Attach the other end of the rubber drainage hose to the inlet of your sink's trap. Again, use a hose clamp to lock it in place. Cut the hose to the correct length with a pair of scissors if necessary.
Apply silicone sealant to the joints between your connectors and your pipe.