You probably just need to find the best posistion to hold your fingers. Theres not really any exersizes you can do.

Try rolling your index finger slightly on its side, and pushing down on the strings a little harder.
Been away, am back
Just keep practising them. Press down hard in order to get all the notes clean. Your fingers will hurt a bit, so rest, then do it again. Do this for 15-30 mins each day to build up strength.

You could also go through chromatic exercises and whatnot to improve general finger strength.
^^^Also after your fingers get hard (before learning any songs) practice random barre chord strumming patterns to help build strength in your wrist. Especially if you play on acoustic.

That will prepare you for when you learn songs with barre chords, so you can play them for a long amount of time without your wrist hurting.
Try to keep your thumb behind the fretboard, roughly centered. Even though this may be a bit harder at first, it will GREATLY help your posture and train your fingers correctly. Also, try resting your guitar on your left leg (assuming you are right handed) and holding the guitar at about a 45 degree angle. This is like the classical guitar form, but don't worry about what it looks like. It is just a more comfortable position and will help you until you get the hand strength you need. The you can go into all cool rock star poses and impress everyone.

Good luck