How can i go to patong beach in Phuket ? from Pattaya in thailand?

You can fly from Pattaya's U-Thaphao Airport to Phuket, Bangkok Airways has a daily flight between the two cities. It is on the expensive side, fares start around 3,700 baht each way. It isn't much further to drive to Suvarnabhumi (BKK) and fly from there, you can fly round-trip on Air Asia for less than the one-way fare from Pattaya. If you don't mind spending more money, Thai Airways and Bangkok Airways also fly that route and IMO are much better airlines. Or as Bob said, you can take a bus.

You can either fly from Bangkok to Phuket or take a bus from Pattaya to Bangkok and then another bus from Bangkok to Phuket.

take taxi to Bangoko airport and fly to phuket, ask the taxi take you to patong beach.