How to sing songs which are high pitch for you.

Singing in the proper scale is important. All singers have a voice range. Most popular singers have a 4 Octave voice range and it takes lot of professional training to achieve that level.  There are few singers who have 6 octave voice range. 
No matter what your vocal range is. You can always sing the song if you practice well. Say you have two octave voice range which is true for most amateur singers, you need to start the song in the lower scale so you can go as high as possible.
Try to catch the tune and other nitty grities of the song. Then start the song in the base pitch, something which is comfortable for you. Go as high as you can while maintaining the composition of the song. 
Before you practice songs which are very High pitch for you to manage, ensure you have done good vocal warmups , open-ed up your voice range by doing lip trills, NG sound exercises and then practice the song and you should be able to achieve good results. 
My personal advise is dont get stuck up on songs which are very high Pitch. Try to sing songs where you are comfortable and you can add emotions to your singing. Extending the vocal range of a singer is a long term process and seldom achieved by few weeks of practice. 

You must be careful singing those high notes. If your throat is clamping down and straining to the point of pain, then you should not be doing it.  You can damage to your vocal chords by forcing high notes that hurt to reach. Having said that continue working to extend your range, but proceed with caution.  Since head voice takes a lot of air to keep the sound stable work on your breath support. There are vocal exercises to help you with this. 

Its absolutely necessary to do the vocal exercises, breathing exercies before you attempt high notes. Now when singing high, your voice cannot have any tension in it. This is the single most important thing you must work on. 

When you start singing in the higher part of your range, if you feel any strain what so ever in your throat, don't go any higher. Drop down to the highest note that you can comfortably sing. Practice in that range until you are 100% comfortable and slowly work up till you can comfortably hit the notes you want. Remember, though, there is a limit to your range. Pushing to far to fast can damage your throat to a point you'll never get there, so proceed with caution.

If you have put more power in your high notes then it may seam like scream or shrill sound, nobody is going to enjoy listening to you singing it. Keep your volumne under control at all times, and not only will you sound better, you'll be able to sing much longer, without tiring out.

Also, remember to switch to your head voice, the higher you go. As the notes get higher, the sound wave the create gets shorter and closer together and do not need as much power to generate, so lighten up on the higher notes. Think of it as a Pyramid. Your power should be on the low notes and decrease as you sing higher.

Finally as I always say listen to yourself by recording and the play it back to yourself. When working on a phrase. Record/Listen identify what is working and not working, and fix it. Then record/listen again until it is right. Then proceed up your range.