There are two kinds of balloons we can receive. The golden balloons are generated by the game and cost 3 tcash to open, after the first one each day.

We can also get free balloons from friends as gifts. Each player can give out five each day. Everybody has a slightly different way of giving their balloons. Some players are very methodical about working down their friend lists and gifting every friend in their turn. Some like to gift more often to friends at lower game levels or to coop members. Others use them as a way to thank players who have helped fill their train or plane crates or zoo requests (found under the Recent Helpers tab). Apart from helping where you can and making sure to hand out your own gifts every day, I'm not sure there is much a player can do to receive more of the gift balloons from other players.