It's a very big subject... Testing. There are many approaches and really, it's not something someone would be able to post in a forum thread for guidance.

I've not used woodling, but it doesn't look like a tetsing framework. More of seeding the db and adding fixtures etc which can be used in combo with testing - I could be wrong, only had a quick glance.

Testing can be VERY confusing at the beginning. Laracasts.com have a heap of videos that taught me a lot and I would highly reccomend jumping on there to get the picture.

Good, well used testing frameworks are: TDD: phpunit (built in to Laravel), phpspec BDD: codeception (my fav), behat