Obviously, you want a low death count, but even within the realm of that, there are certain situations where you may have a higher death count which is fine.
Take Braum and Leona for example, both are initiator tanks, chances are, or should be the case, you're going to have a much higher death count using them as oppose to someone like Nami or Lulu who stand back and help assist players in the fight.
The best advice I can give for you, if you're learning support, is to stick first with low-risk champions. In other words, use champions whom are not required to start the fight, or enter the fray of the fight itself, Nami (if you can land her bubbles), Annie, Lulu, Morgana, are all good ones.
Once you got a good handle, it becomes easier to learn how to play 'carry' supports, Blitz, Thresh, Zyra, Leona, and Braum all come to mind. The critical part of learning these champions is recognizing when is best time to initiate, (Braum's ult, Thresh and Blitz's hook, Zyra's AoE denial, Leona's AoE stun.). If you initiate poorly, your team is going to pay dearly.
I will also warn you, ignore what many of people who are critical of you are going to say. Many people claim support is useless when the reality is far from the truth, but a good support can have a huge impact on winning the game, and vice versa, can cause a game to be lost. Focus on communicating with ADC, and don't worry about negativity from other people, the job of a support is a pretty thankless one in most cases.
So yeah, just practice, and welcome to the world of supports :D