How can I go from Goa airport to Palolem?
The easiest way is to get a taxi. Otherwise you can get a public bus to Vasco, and then change for another bus to Margao and from there take a bus to Palolem.
How I can go from Panaji?
Panaji to Margao by bus and then again take a bus from Margao bus stand to reach Palolem.
Canacona railway station is the nearest railway station. There are overnight trains from Mumbai to Canacona, but always check whether it is stopping at Canacona as some trains coming to Goa stops in Margao