Earn Airline Miles

I often travel to Denmark and I was wondering what would be the best way to earn miles that I can use later to a free ticket.
I know he is the Star Alliance group that has these companies:
Air Canada #
Air New Zealand #
ANA #
Asiana Airlines #
# Austrian
# Bmi
# LOT Polish Airlines
Lufthansa #
# Scandinavian Airlines
# Singapore Airlines
# South African Airways
# Spanair
SWISS #
# TAP Portugal
# THAI
# United
# U.S. Airways

Are there other groups with different types of airlines??

another way to earn airline miles is to get a credit card that gives miles for purchases and does not charge fees.
Capital One does not charge a fee.

See also American Express credit card, but they pay.

steal a lot.

I say a visa will be the best but if u are a member of Star Alliance and United do u miles for shopping on the DFT and Netflix or groceries at Safeway, VONS, and Pavililians.