What's the meaning of "get one's finger in the air"?

You "get your finger in the air" means to "go with the crowd", "go with the flow". You want to see, where the wind is coming from - usually by wetting the finger before. A person "putting his finger in the air" is unlikely to come up with original, individual ideas or solutions. And decisions are made unscientifically, without backing evidence.

Examples:

The "finger in the air" approach to enterprise-wide IT where you have no clear view of cost or quality is to go with Microsoft.

Stick a finger in the air of local politics these days, and you'll probably detect a strong wind pushing against new health care reform efforts like Measure ...

See here.

In my experience, the phrase "put a finger in the air," used in a business and IT context, is another way of saying "make a high-level estimate." It's often an "order of magnitude" estimate (e.g., five or six figures; days/weeks/months), based on the speaker's experience or gut. It is another term for "SWAG" (Sophisticated Wild-Ass Guess). It does come from the practice of estimating the wind's direction by wetting one's finger and holding it up in the air.