How can I write an effective Google AdWords copy?

You have to be specific about what you are writing through explaining the main message, and in order to do so you have to use specific keywords that can help you make your message more clear.
Try to be unique and stand out from your competitors, use ad format that is catchy and attractive.

The best way is to target content related Keywords.
Try to include Keywords in the Heading and description of the ad it will improve your keyword Quality Score.
If your Quality score is 8/10 Google will automatically charge less Cost Per Click with more top impressions.
The third and very important is Call to action (CTA).
Register Now! Contact Us! etc You can also use extensions in your ad to get more attraction .
Phone Number, your Google Place etc

Trying using relevant keywords and have a proper landing page.
Make sure your copy is straight to the point with "Call to Action" Provide statements like "Register now, Join us now, Check out this free..." And try to use relevant keywords in the title! Good luck!

Try as you can to put the keywords that you are targeting in the ads title and ads description and put call to action

Based on personal experience; ALWAYS add, either a discount % or [value] OFF! -- Phone number! -- and from George's answer: Make sure your copy is straight to the point!

1. Write Specific Ads for Specific Keywords

2. Cater Ad Copy to Different Buyer Needs

3. Ad Copy Should Be Appropriate In "Feel" To the Industry Category

4. Consider the Buy Cycle

5. Analyze Paid Search Results

6. Ensure PPC Data is Statistically Significant

7. Carry Over Ad Copy Keywords to Landing Pages

8. Keep Testing Ad Copy

9. Spend Time Creating Killer Ad Copy

10. Think Outside the Box