Total Beginner - Terrified of belaying

Find a local climbing club or group, buy some beers for the folks and talk to members who they trust belaying, watch their technique and ask for a belay only after they are no longer a stranger.
Learn some techniques to manage your anxiety.
And consider the possibility that this sport with inherent risk that can never be reduced to zero may not be a good fit for you.

Midori O wrote: it's just the whole random pairing up that seems to be my worry point.

It's not like most people show up at the gym and climb with whoever is available. You generally have a regular partner(s) that are friends that you go with. So you should have some confidence that your friend can belay because you saw them do it before and also that they have some vested interest in not killing you. 

Midori O wrote: Hello,

I'm a total beginner at climbing. I'm moving to a big city in September for school and have wanted to climb forever, but there was never a place. Now I have the choice of several gyms to learn!

Unfortunately, I'm terrified of belaying... the thought that my life is in the hands of some stranger I don't know is really creepy. It's easy to get distracted or be looking at their phone... Our country recently legalized drugs, so that's another concern. I know they have auto belayers at some of the gyms, but only for 2 or 3 different courses, so I feel like it would bet old fast. Also, is it possible to do auto belayers with lead climbing?

Any suggestions would be appreciated!

This is a legit fear.  Especially when you are new to the sport.  It's hard to trust someone that you barely know with your life.