The new (sort of) support

These guys have already done a great job giving advice, but a few things they haven't really covered:

1) Stick with your team, or at least one other player. Quite often gankers on your team just need your slow or stun in order to secure a kill, so get used to going with them in ganking spots and trying to get assists - it will get you used to playing more aggressively.

2) Remember that as a hard support it is ok to die sometimes - you're the least farm/xp dependent player on your team, so if you die but manage to help get a kill on an enemy hero, it will almost always be a "good trade" for your team. For example, you die but so does their carry - this will help your team. Just spend any gold you have first.

3) It could be worth playing quite an aggressive support like Vengeful Spirit. Her abilities are reasonably straight forward, but Nether Swap can basically be suicide. However, as of point 2), if you can swap an enemy carry and get them killed, this is a good trade for your team.

Being willing to be patient and relatively passive is a good skill for a hard support, so not something you want to lose, but try to learn the situations where you can achieve more, even if there is some risk involved.