So, the best option is to find a couple of friends (at least one willing to tank) and learn there. That’s not always easy, and it’s a bit harder on a starter account because of the social restrictions.
You may want to go back and try battlegrounds again. They can be brutal, but they make for a good place to learn under pressure. I think you can queue for epic battlegrounds at 20, and those are much lower pressure because there are so many players. (They also make for better healing learning as all those extra people mean you might not get focused down quite as quickly as well.)
When it comes to healing, your user interface makes a huge difference. You may want to look into some more healer-focused party/raid frame addons. However, there are some settings that can make the default UI more healer friendly. If you go into the raid profiles setting, there’s a checkbox at the top to use “raid style party frames.” That will turn your party frames into HP boxes and stack them together making it easier to quickly see useful info. There are some setting you can play with. (Unfortunately, you’ll need to be in a party to actually see the frames, and if you can’t find someone to party up with you, you can try and mess with the settings in an Epic Battleground.)
Once the frames are up, they’ll be on the side of the screen near a thin grey bar. The bar can expand, and one of the options is to unlock the frames. That lets you move them around on the screen and set how high the bars will stack before it starts a new row.
Most healers use some combo of mouseover macros and/or click casting addons. A basic mousevoer macro will look like this:
#showtooltip
/cast [@mouseover, help, nodead][]Flash of Light
This allows you to heal someone by hitting the keybind attached to the macro when the mouse if hovering over either the players unit frame or their character model out in the world. It saves you the step of actually targeting them (and lets you keep a different target like the boss.)
Click casting addons (Clique is a popular one, and some raid frame addons like Vuhdoo have it build in as well) will let you do something similar, but they won’t work over player models out in the world. However, unlike mouseover macros, they will work with mouse button keybinds. (Mouseover macros don’t work with mouse button keybinds as frame “eat” mouse clicks.)