I'm going to be totally real with you.
There's only ONE way to guarantee you'll be able to get better with high notes.
Take some formal training.
Yes, vocal coaches are expensive. But taking an online singing course doesn't have to be. And some of the courses are just like having a private coach.
Consider it if you're serious about improving your range and hitting those highs.
Before you begin exercises to help you hit that height easily, you need to understand what using your chest and your head means.
A proper balance of the two creates a high pitched note in your vocal chords.
This is essentially where the sounds created from using your chest are made.
This would be the sounds you can hear if you compress the chest and try to create a sound between your vocal chords and mouth.
Why Does That Matter?
You will begin to understand these better when you begin singing, but for now you should know that you get to your higher notes from your chest.
The best way to practice these is to use Staccato scales.
Staccato is singing set of disconnected notes broken down into each note being sung separately, almost like saying “Do Re Mi…” short and fast.
If the notes are sung in a long and continuous manner, it is called a Legato.
What to Practice
Practice Staccato by singing short sounds like “Ti Ti Ti…” up and down whatever scale you prefer.
You will be achieve to achieve what you are aiming for much easily if you practice this exercise.
Once you've got that down then slowly transition to legato notes.
Why Should I Do That?
This will help you to understand your chest voice which is very important since you create most of the high pitched notes from this area.
Using your head sounds much deeper allowing you to create bass or harmonic section in the lower tones.
Things To Look Out For
Sometimes you may find yourself choking or becoming shrill when you try to touch the highest points in a song.
This is when you are doing it in the wrong way. You should not compress your vocal chords. Instead you should be compressing your chest and letting in very little air through.
Now, some people relate to a high note being in Falsetto, but that is again a different way of vocalizing.
While singing higher should not crack your vocals, many beginners often try and strain to the point that it does crack.
Practice the exercise above at least an hour daily. You will get the hang of it very easily and singing high notes will not seem as difficult.
If you want to learn more about using your head vocals read this.