For LFR, nobody is going to tell you who/what to heal. I do recommend getting an add-on that shows frames for everyone in the raid, if you don’t have any yet. Then just heal people who are injured. That’s really all there is to it. As was pointed out above, LFR is designed to be completed by 30 strangers who barely talk to each other.
For more “serious” raiding within a guild, each guild has their own way of doing things. But generally there is likely to be a raid leader who assigns specific roles to specific people. Holy Priests fall pretty well in the middle with regard to excelling at either single-target or group healing. Therefore, your assignment, if you get one, would depend on a lot of different factors, such as the composition of the rest of the raid, your gear, your demonstrated competence, etc.
Short version: If you want to do LFR, just queue when you get to 120 (and the required iLevel) and heal away. If you want to do normal/heroic/mythic raiding, find a guild and make clear what your goal is. They will help you with what you need to know.