I think Healbot is still around, but I'm not totally sure it's as widely used as it once was. Vuhdo basically is the same as far as I know. It's really easy to set up the key bindings. Just open the mod menu and your spell list and you can drag and drop to the key bindings you want. I can't remember the set up I have on my priest as I haven't play it in a while, but for my Shaman I put my most frequently used spells for my base clicks, add shift for my next most used, then ctrl, then alt for whatever I have left over like rezzing. When I set up my key bindings I like to stand around for a while to get a feel for them just on my own. The set up doesn't always work comfortably when actually playing so either ask for the group to stop for a minute to adjust to just make a note to yourself to do it afterwards or during some downtime.
In terms of actually healing I don't like to let people get too much below 75% health (unless I'm really bored and want to see how fast I can get them back to 100%). Most often I'll start healing people when they hit even 90%, that way if thing get a bit out of control or the tank loses threat it's less of an issue. Might be overkill, but I rarely lose anyone unless the shit really hits the fan. I like to keep Earth Shield (Shaman ability. I think there's a priest bubble that's similar) on my tank as they are usually taking the most direct damage, as well as a HoT (heal over time) if I can spare it. If the tank doesn't need it or there is someone else that's taking damage consistently I put my HoT on them for support. Don't feel obligated to heal hunter pets if you set up your healing frame to show them. I'm sure hunters appreciate when healers do heal their pets, but they should be your lowest priority and only if you have mana to spare. Also, and this is important, don't forget to heal yourself. I am so bad for that. I get tunnel vision in keeping everyone else alive that sometimes I find my heal had dropped lower than I would like.
If there's not much going on and you don't need to heal anyone don't be afraid to help out the dps. A little bit of extra damage is always welcome.
I really love healing. It's a fun challenge and can keep you on your toes at times. I hope you go for it and give it a go. Leveling up as a healer makes it so much faster to get in dungeons. If you have any other questions I'm happy to answer what I can. Icy-Veins is also pretty helpful, though it's directed more for characters at level cap.