Hi natalya
I am assuming that you are flying on Qantas mostly with some flights with other oneworld carriers (such as BA, Cathay, American and others) - would that be correct?
If so and if you want to earn Qantas FF points then just go to the qantas webiste and follow the links to join the Qantas scheme, then call your travel agent or Qantas and get them to link your FF number to your booking.
Note is costs $82.50 to join the Qantas FF scheme.
There are a lot more considerations and if you tell us your routing, carriers and class of service people can make some really useful recommendations to you.
Cheers
S