To Get is the normal form and would be best for everyday use. However book titles are allowed artistic license. Regarding the to Getting forms, I would think of it this way: 1) The Essential Guide to (doing something) + (which is) Getting Your Book Published and 2) The Guide to (doing something) + (which is) Getting it On In these examples each phrase can stand on its own, but you have follow ...

Understanding the Context

Start cooking with ease! Explore beginner cookbooks packed with simple recipes, essential tips, and affordable ingredients to make delicious meals at home. Getting started with cooking at home can ... So, I like getting/ to get to the station in plenty of time.

Key Insights

In grammar in use book, the bold part has been considered as correct answer. I am wondering why. What is more, would you show me a more detailed explanation or another synonym for the following?-- I have some problem with especially using the preposition in along with plenty of time. Which one is correct- He did not succeed to get the job though he tried his level best. He did not succeed in getting the job though he tried his level best.

Final Thoughts

Book says second one is correct. Yes there is a difference. Trees are getting cut down refers to an action that is in progress. Someone is cutting the trees. It is the form encountered more frequently. Trees getting cut down can be used in the context of an intended action.

To explain: If someone has decided to cut some trees down, they may be referred to as the trees getting cut down. The trees are still standing at the time ...