In order to Shield, you have to Hover under or fly continually into the bottom of a Platform, or the ceiling. The advantage of doing this is that Balloon Birds and other players cannot pop your Balloons as easily because of the Platform or the Ceiling which prevents them from getting above you and coming down. This tactic is usually considered "cheap", because it can easily cause both players to be rendered unbeatable, which when players are playing competitively, can be somewhat frustrating.
However, when you are Shielding, you must be careful of Bouncing, Sparks, and Arrows. Sparks and Arrows, which come on-screen to motivate players to clear phases faster, can immediately kill the player. Bouncing, which is even more pronounced with one Balloon, can easily cause gaps in the player's protection, allowing enemies or other players to pop your Balloons.