Make sure you wash your hands really good, and keep them damp. don't wipe them off with a paper towel, instead use a clean dry soft cloth. like i said, keep them damp.
Then, clean the phone, and wash your hands again. Make sure you clean the phone under a really bright light so you can see EVERYTHING. Use the soft rag that came with the phone to clean the screen and whatnot, then use the plastic dirt remover that came with the screen protector (they almost all come with one).
Then, take the new screen protector, and barely peel back the bottom. Line it up perfectly, then apply just the bottom lip. Slowly peel back the rest a really small amount, and apply that, and keep going til it's all the way on.
Remember as you are applying it, to use your finger to also smooth out bubbles while you are applying it. If you're doing it right, you shouldnt have ANY bubbles at all, and it should go on fairly easily without difficulty.
I recommend using "power support" brand screen protectors, and buy an anti-glare one.... you can't go wrong with it.