There are no direct airlines connecting India to Perth. Connecting flights however are available very easily and airlines such as Air Asia, Malaysian Airlines, Singapore Airlines, Thai Airways etc. have various routes to Perth from India.
Perth Airport has daily flights running routes domestically and internationally. International airlines such as Emirates, Cathay Pacific, Southern China Airlines, Singapore Airlines among several others connect Perth to all major cities around the glob via connecting and direct flights.
While cities in Western Australia have easy access to Perth via roads, trips to other major cities such as Adelaide, Sydney, Melbourne et al are not feasible due to really long driving distances.
Perth is connected to nearby cities fairly well via rail. The Indian Pacific rail connects Perth all the way across Australia to Sydney via Adelaide. Though the trip is long, it is one of immense scenic beauty. Cities close by are connected via local trains running twice or thrice a day.
From nearby cities. Talk about connectivity, compare different services (if any)
A few international cruisers such as Queen Victoria dock at the Freemantle harbour. Other passenger ships to Perth are now few and far between.