Really, to keep your teammates alive better, you have to be aware of what is going on. Pay attention to your surroundings. Think about where the mobs are, where your teammates are and think about Line of Sight (LOS) with the mobs.

Apart from being aware, it helps if you take care of yourself. Keep your implants of the highest caliber you can afford. This also applies to your weapons and heals. Make sure to keep your NanoInit. high so that your heals are cast fast.

Think about when to cast team heals and when to cast target heals. Don't cast a team heal when there is just a single teammate that is taking all the hits. Also, don't target heal a teammate when he/she barely has any damage. They could REALLY need a heal while you're waiting on the heal recharge.

Play smart and you'll be excellent at keeping your team alive :)