You have to get status on one airline. For example, 50K on United gives you Premier Executive, which is also Star Alliance Gold.

The status level that equates to Star Silver and Star Gold is different on different programs. I have read, for example, that it's easier to obtain Gold through bmi.

So you need to concentrate your mileage earning on one airline to reach the threshold for that airline. You really need to strategize what other benefits that you want (e.g., upgrades) and what routes and airlines you will be flying to determine the best airline on which to pursue the status.

In answer to your other questions: Once you hit Gold, you receive the benefits on all Star Alliance airlines. It takes effect immediately, although for some benefits (e.g., access to lounges in far-flung places), you might need as a practical matter to wait until you receive your membership card with the Star Gold designation on it.