I need to change several habits but whenever I do something that is new to me, I get a little stressed.

That happens to everyone, including me. You need to understand one thing -- change is a part of life.

I am no expert either nor have I read any book on this topic however what I learnt from my experience is change should be slow. Any drastic change can cause problems sometimes. I substantiate this statement by giving you the example of an industry practice for adopting changes called Kaizen.

I quote from some website:

In Japanese, the definition of Kaizen is "improvement" and particularly, "Continuous Improvement"-- slow, incremental but constant.

Now, time to apply this to your real life, the simple way.

Step 1. Identify what you need to change.
Step 2. Identify if that change is even necessary.
Step 3. If it is, create phases to implement that change.

Here is a simple example:
Assuming you are addicted to video games and this is harming your productivity. You want to learn something new but can not get yourself to. Change the thing in phases as follows:

Step 1. Allocate time for yourself to play games. (Say, 2 hours at the start)
Step 2. Identify something that is new yet closely related to gaming -- how about learning how to design a game ?
Step 3. Allocate 15 mins a day from your gaming time to this new task.
Step 4. Gradually increase the time you dedicate to the new task.
Step 5. Target to meet a realistic deadline

I have been using this technique so far and works for me. Your thoughts on my answer are welcome :)