First of all, what OS are you running? What java version? You might not need to update your LWJGL to 2.9 manually like me (remember I was unsuccessful at fixing Hexxit). Also, your trying to run the new Tekkit right (the one without industrial craft 2)?
Also, here's the instructions you asked for (I made them simple stupid in case a 10 year old finds this topic and reads this):
[stuff you probably already know but I included this just in case]
Download LWJGL from here (scroll down to the download link).
Open the bin folder of the tekkit folder within .technic (or just technic if your using a mac).
[more important instructions]
After you opened the bin folder, open lwjgl-2.9.0.zip, extract all its contents, and open the the folder called jar (the location is different depending on how you extracted it).
Now copy these files and only these files from the jar folder into the aforementioned bin folder: lwjgl_util.jar, lwjgl.jar, jinput.jar.
Now exit the jar folder and open the native folder (the called "native" from the .zip) and within it, there's folders named after operating systems. Choose the folder corresponding to whatever OS you use and copy all the files within.
Paste these files in the folder named "natives" in bin and test your Tekkit.
You can find similar instructions online if you need more clarification. Let me know if these instructions worked for you.