I tried a vocal teacher once, and they do definitely help, but in all honesty it just got to be too expensive for what I was trying to do. So instead of hiring another cheaper vocal coach (you never want to hire cheap cuz that probably means the suck as a singing instructor) I tried to find some self-teaching resources.
The best thing I can recommend to you is also try some online singing lessons like I am. I'm new to singing like I said but I found these to be super helpful. I like that I can just practice the parts I'm struggling with without having to wait for my vocal coach to get there on his or her schedule.
I found
this page on singing lessons online with some useful comparisons. I ended up going for
this particular option and found it to be absolutely fantastic. It's helping me out so much. I'm still just starting out but I can already tell the difference.
But seriously, just try out something. You don't have to use the same singing lessons I did, but I find them to be much more useful than singing teachers. Maybe I just had a bad experience, but let me tell you being able to go at your own pace and focus on the singing training you want is so much better than a person.
The only draw back is you don't get immediate feedback from a real live individual. But let's be real, you can't exactly tell if your vocal coach is doing the right thing with you. But with online singing lessons you can tell if it's worth it by all the feedback and reviews about it posted online.
Here's another good option if the one I picked isn't the right one for you. If you do end up trying something out, let us know how it worked out.