This should come quite naturally.
Personally I found it the easiest way to just play the second event, called "New Leaf Open". It contains 9 holes of which the first 5 are pretty easy to get a birdie on.
Try to use your golfers special ability to make this even easier.
I used Frank when I got it on the first hole with Astrid as my caddie.
Here is what I did
1. Hit the ball at the top (You can adjust the hit area with the d-pad) and use your special ability - This should get you pretty far on the fairway.
2. Hit the ball at the bottom centre (this will make the ball stop closely to it's landing position) - If you hit it perfectly you should get the ball relatively close to the hole
3. Use Astrid as a caddy and make use of her putting preview (this should make the putting a piece of cake when your approach to the hole wasn't too bad) - You should have completed it with 3 strikes which awards you with a birdie and the achievement
If you are having problems with this still just keep playing till you get some better equipment and some boosters to make this even easier, but you should not have to many problems on the first hole.
Hope this helps you guys. If there is anything off with this solution please let me know in the comments ;-)